AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution
Perverse Sheaves and Applications to Representation Theory
About this Title
Pramod N. Achar, Louisiana State University, Baton Rouge, LA
Publication: Mathematical Surveys and Monographs
Publication Year:
2021; Volume 258
ISBNs: 978-1-4704-5597-2 (print); 978-1-4704-6668-8 (online)
DOI: https://doi.org/10.1090/surv/258
Table of Contents
Download chapters as PDF
Front/Back Matter
Chapters
- Sheaf theory
- Constructible sheaves on complex algebraic varieties
- Perverse sheaves
- Nearby and vanishing cycles
- Mixed sheaves
- Equivariant derived categories
- Kazhdan-Lusztig theory
- Springer theory
- The geometric Satake equivalence
- Quiver representations and quantum groups
- Category theory and homological algebra
- Calculations on $\mathbb {C}^n$
- Quick reference
- Revêtements étales et groupe fondamental (SGA 1), Documents Mathématiques (Paris) [Mathematical Documents (Paris)], vol. 3, Société Mathématique de France, Paris, 2003 (French). Séminaire de géométrie algébrique du Bois Marie 1960–61. [Algebraic Geometry Seminar of Bois Marie 1960-61]; Directed by A. Grothendieck; With two papers by M. Raynaud; Updated and annotated reprint of the 1971 original [Lecture Notes in Math., 224, Springer, Berlin; MR0354651 (50 #7129)]. MR 2017446
- Théorie des topos et cohomologie étale des schémas. Tome 1: Théorie des topos, Lecture Notes in Mathematics, Vol. 269, Springer-Verlag, Berlin-New York, 1972 (French). Séminaire de Géométrie Algébrique du Bois-Marie 1963–1964 (SGA 4); Dirigé par M. Artin, A. Grothendieck, et J. L. Verdier. Avec la collaboration de N. Bourbaki, P. Deligne et B. Saint-Donat. MR 0354652
- Théorie des topos et cohomologie étale des schémas. Tome 3, Lecture Notes in Mathematics, Vol. 305, Springer-Verlag, Berlin-New York, 1973 (French). Séminaire de Géométrie Algébrique du Bois-Marie 1963–1964 (SGA 4); Dirigé par M. Artin, A. Grothendieck et J. L. Verdier. Avec la collaboration de P. Deligne et B. Saint-Donat. MR 0354654
- A. Grothendieck et al., Cohomologie $l$-adique et fonctions $L$, Séminaire de Géometrie Algébrique du Bois-Marie 1965–1966 (SGA 5), Lecture Notes in Mathematics, no. 589, Springer-Verlag, 1977.
- Groupes de monodromie en géométrie algébrique. II, Lecture Notes in Mathematics, Vol. 340, Springer-Verlag, Berlin-New York, 1973 (French). Séminaire de Géométrie Algébrique du Bois-Marie 1967–1969 (SGA 7 II); Dirigé par P. Deligne et N. Katz. MR 0354657
- Pramod N. Achar, Anthony Henderson, Daniel Juteau, and Simon Riche, Weyl group actions on the Springer sheaf, Proc. Lond. Math. Soc. (3) 108 (2014), no. 6, 1501–1528. MR 3218317, DOI 10.1112/plms/pdt055
- Pramod N. Achar, Anthony Henderson, Daniel Juteau, and Simon Riche, Modular generalized Springer correspondence I: the general linear group, J. Eur. Math. Soc. (JEMS) 18 (2016), no. 7, 1405–1436. MR 3506603, DOI 10.4171/JEMS/618
- Pramod N. Achar, Anthony Henderson, Daniel Juteau, and Simon Riche, Constructible sheaves on nilpotent cones in rather good characteristic, Selecta Math. (N.S.) 23 (2017), no. 1, 203–243. MR 3595892, DOI 10.1007/s00029-016-0236-z
- Pramod Achar, Anthony Henderson, Daniel Juteau, and Simon Riche, Modular generalized Springer correspondence II: classical groups, J. Eur. Math. Soc. (JEMS) 19 (2017), no. 4, 1013–1070. MR 3626550, DOI 10.4171/JEMS/687
- Pramod N. Achar, Anthony Henderson, Daniel Juteau, and Simon Riche, Modular generalized Springer correspondence III: exceptional groups, Math. Ann. 369 (2017), no. 1-2, 247–300. MR 3694647, DOI 10.1007/s00208-017-1524-4
- Pramod N. Achar, Anthony Henderson, and Simon Riche, Geometric Satake, Springer correspondence, and small representations II, Represent. Theory 19 (2015), 94–166. MR 3347990, DOI 10.1090/ert/465
- Pramod N. Achar, Shotaro Makisumi, Simon Riche, and Geordie Williamson, Koszul duality for Kac-Moody groups and characters of tilting modules, J. Amer. Math. Soc. 32 (2019), no. 1, 261–310. MR 3868004, DOI 10.1090/jams/905
- Pramod N. Achar and Carl Mautner, Sheaves on nilpotent cones, Fourier transform, and a geometric Ringel duality, Mosc. Math. J. 15 (2015), no. 3, 407–423, 604 (English, with English and Russian summaries). MR 3427432, DOI 10.17323/1609-4514-2015-15-3-407-423
- Pramod N. Achar and Laura Rider, Parity sheaves on the affine Grassmannian and the Mirković-Vilonen conjecture, Acta Math. 215 (2015), no. 2, 183–216. MR 3455233, DOI 10.1007/s11511-016-0132-6
- Dean Alvis and George Lusztig, On Springer’s correspondence for simple groups of type $E_{n}$ $(n=6,\,7,\,8)$, Math. Proc. Cambridge Philos. Soc. 92 (1982), no. 1, 65–78. With an appendix by N. Spaltenstein. MR 662961, DOI 10.1017/S0305004100059703
- H. H. Andersen, J. C. Jantzen, and W. Soergel, Representations of quantum groups at a $p$th root of unity and of semisimple groups in characteristic $p$: independence of $p$, Astérisque 220 (1994), 321 (English, with English and French summaries). MR 1272539
- Aldo Andreotti and Theodore Frankel, The Lefschetz theorem on hyperplane sections, Ann. of Math. (2) 69 (1959), 713–717. MR 177422, DOI 10.2307/1970034
- Donu Arapura, Algebraic geometry over the complex numbers, Universitext, Springer, New York, 2012. MR 2895485, DOI 10.1007/978-1-4614-1809-2
- M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0242802
- G. Barthel, G. Göringer, J. Duskin, R. Fittler, H. Acuña, R. Gergondey, J.-L. Verdier, and M. Zisman, Séminaire Heidelberg-Strasbourg, 1966/1967: Dualité de Poincaré, Publ. I.R.M.A., no. 3, Institut de Recherche Mathématique Avancée, Strasbourg, 1969.
- Pierre Baumann and Simon Riche, Notes on the geometric Satake equivalence, Relative aspects in representation theory, Langlands functoriality and automorphic forms, Lecture Notes in Math., vol. 2221, Springer, Cham, 2018, pp. 1–134. MR 3839695
- A. A. Beĭlinson, How to glue perverse sheaves, $K$-theory, arithmetic and geometry (Moscow, 1984–1986) Lecture Notes in Math., vol. 1289, Springer, Berlin, 1987, pp. 42–51. MR 923134, DOI 10.1007/BFb0078366
- A. A. Beĭlinson, On the derived category of perverse sheaves, $K$-theory, arithmetic and geometry (Moscow, 1984–1986) Lecture Notes in Math., vol. 1289, Springer, Berlin, 1987, pp. 27–41. MR 923133, DOI 10.1007/BFb0078365
- A. A. Beĭlinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces, I (Luminy, 1981) Astérisque, vol. 100, Soc. Math. France, Paris, 1982, pp. 5–171 (French). MR 751966
- A. Beĭlinson and V. Drinfel$’$d, Quantization of Hitchin’s integrable system and Hecke eigensheaves, preprint.
- Alexandre Beĭlinson and Joseph Bernstein, Localisation de $g$-modules, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 1, 15–18 (French, with English summary). MR 610137
- Joseph Bernstein and Valery Lunts, Equivariant sheaves and functors, Lecture Notes in Mathematics, vol. 1578, Springer-Verlag, Berlin, 1994. MR 1299527, DOI 10.1007/BFb0073549
- A. Białynicki-Birula, Some theorems on actions of algebraic groups, Ann. of Math. (2) 98 (1973), 480–497. MR 366940, DOI 10.2307/1970915
- Gebhard Böckle and Chandrashekhar Khare, Mod $l$ representations of arithmetic fundamental groups. I. An analog of Serre’s conjecture for function fields, Duke Math. J. 129 (2005), no. 2, 337–369. MR 2165545, DOI 10.1215/S0012-7094-05-12925-8
- Cédric Bonnafé, Éléments unipotents réguliers des sous-groupes de Levi, Canad. J. Math. 56 (2004), no. 2, 246–276 (French, with English and French summaries). MR 2040915, DOI 10.4153/CJM-2004-012-0
- A. Borel and J. C. Moore, Homology theory for locally compact spaces, Michigan Math. J. 7 (1960), 137–159. MR 131271
- A. Borel and N. Spaltenstein, Sheaf theoretic intersection cohomology, Intersection cohomology (Bern, 1983) Progr. Math., vol. 50, Birkhäuser Boston, Boston, MA, 1984, pp. 47–182. MR 788176, DOI 10.1007/978-0-8176-4765-0_{5}
- Armand Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. (2) 57 (1953), 115–207 (French). MR 51508, DOI 10.2307/1969728
- Armand Borel, Seminar on transformation groups, Annals of Mathematics Studies, No. 46, Princeton University Press, Princeton, N.J., 1960. With contributions by G. Bredon, E. E. Floyd, D. Montgomery, R. Palais. MR 0116341
- Armand Borel, Sous-groupes commutatifs et torsion des groupes de Lie compacts connexes, Tohoku Math. J. (2) 13 (1961), 216–240 (French). MR 147579, DOI 10.2748/tmj/1178244298
- Armand Borel, Linear algebraic groups, 2nd ed., Graduate Texts in Mathematics, vol. 126, Springer-Verlag, New York, 1991. MR 1102012, DOI 10.1007/978-1-4612-0941-6
- A. Borel, P.-P. Grivel, B. Kaup, A. Haefliger, B. Malgrange, and F. Ehlers, Algebraic $D$-modules, Perspectives in Mathematics, vol. 2, Academic Press, Inc., Boston, MA, 1987. MR 882000
- A. Borel and et al., Intersection cohomology, Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2008. Notes on the seminar held at the University of Bern, Bern, 1983; Reprint of the 1984 edition. MR 2401086
- Walter Borho and Robert MacPherson, Représentations des groupes de Weyl et homologie d’intersection pour les variétés nilpotentes, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 15, 707–710 (French, with English summary). MR 618892
- Walter Borho and Robert MacPherson, Partial resolutions of nilpotent varieties, Analysis and topology on singular spaces, II, III (Luminy, 1981) Astérisque, vol. 101, Soc. Math. France, Paris, 1983, pp. 23–74. MR 737927
- Raoul Bott and Loring W. Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics, vol. 82, Springer-Verlag, New York-Berlin, 1982. MR 658304
- N. Bourbaki, Éléments de mathématique. Topologie générale. Chapitres 1 à 4, Hermann, Paris, 1971. MR 0358652
- Tom Braden, Hyperbolic localization of intersection cohomology, Transform. Groups 8 (2003), no. 3, 209–216. MR 1996415, DOI 10.1007/s00031-003-0606-4
- Glen E. Bredon, Sheaf theory, 2nd ed., Graduate Texts in Mathematics, vol. 170, Springer-Verlag, New York, 1997. MR 1481706, DOI 10.1007/978-1-4612-0647-7
- Michel Brion, Linearization of algebraic group actions, Handbook of group actions. Vol. IV, Adv. Lect. Math. (ALM), vol. 41, Int. Press, Somerville, MA, 2018, pp. 291–340. MR 3888690
- Kenneth S. Brown, Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York-Berlin, 1982. MR 672956
- F. Bruhat and J. Tits, Groupes réductifs sur un corps local, Inst. Hautes Études Sci. Publ. Math. 41 (1972), 5–251 (French). MR 327923
- Jonathan Brundan, Quiver Hecke algebras and categorification, Advances in representation theory of algebras, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2013, pp. 103–133. MR 3220535
- Jean-Luc Brylinski, Transformations canoniques, dualité projective, théorie de Lefschetz, transformations de Fourier et sommes trigonométriques, Astérisque 140-141 (1986), 3–134, 251 (French, with English summary). Géométrie et analyse microlocales. MR 864073
- J.-L. Brylinski and M. Kashiwara, Kazhdan-Lusztig conjecture and holonomic systems, Invent. Math. 64 (1981), no. 3, 387–410. MR 632980, DOI 10.1007/BF01389272
- Roger W. Carter, Finite groups of Lie type, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1985. Conjugacy classes and complex characters; A Wiley-Interscience Publication. MR 794307
- David H. Collingwood and William M. McGovern, Nilpotent orbits in semisimple Lie algebras, Van Nostrand Reinhold Mathematics Series, Van Nostrand Reinhold Co., New York, 1993. MR 1251060
- Brian Conrad, Deligne’s notes on Nagata compactifications, J. Ramanujan Math. Soc. 22 (2007), no. 3, 205–257. MR 2356346
- Mark Andrea A. de Cataldo, Decomposition theorem for semi-simples, J. Singul. 14 (2016), 194–197. MR 3595140, DOI 10.1007/s11856-006-0006-2
- Mark Andrea A. de Cataldo and Luca Migliorini, The hard Lefschetz theorem and the topology of semismall maps, Ann. Sci. École Norm. Sup. (4) 35 (2002), no. 5, 759–772 (English, with English and French summaries). MR 1951443, DOI 10.1016/S0012-9593(02)01108-4
- Mark Andrea A. de Cataldo and Luca Migliorini, The Hodge theory of algebraic maps, Ann. Sci. École Norm. Sup. (4) 38 (2005), no. 5, 693–750 (English, with English and French summaries). MR 2195257, DOI 10.1016/j.ansens.2005.07.001
- C. De Concini, G. Lusztig, and C. Procesi, Homology of the zero-set of a nilpotent vector field on a flag manifold, J. Amer. Math. Soc. 1 (1988), no. 1, 15–34. MR 924700, DOI 10.1090/S0894-0347-1988-0924700-2
- Pierre Deligne, Théorie de Hodge. I, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 425–430 (French). MR 0441965
- Pierre Deligne, Théorie de Hodge. II, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 5–57 (French). MR 498551
- Pierre Deligne, La conjecture de Weil. II, Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137–252 (French). MR 601520
- P. Deligne, Un théorème de finitude pour la monodromie, Discrete groups in geometry and analysis (New Haven, Conn., 1984) Progr. Math., vol. 67, Birkhäuser Boston, Boston, MA, 1987, pp. 1–19 (French). MR 900821, DOI 10.1007/978-1-4899-6664-3_{1}
- P. Deligne and J. S. Milne, Tannakian categories, Hodge cycles, motives, and Shimura varieties, Lecture Notes in Math., no. 900, Springer-Verlag, 1982, pp. 101–228.
- Michel Demazure, Invariants symétriques entiers des groupes de Weyl et torsion, Invent. Math. 21 (1973), 287–301 (French). MR 342522, DOI 10.1007/BF01418790
- Michel Demazure, Désingularisation des variétés de Schubert généralisées, Ann. Sci. École Norm. Sup. (4) 7 (1974), 53–88 (French). MR 354697
- Bangming Deng, Jie Du, Brian Parshall, and Jianpan Wang, Finite dimensional algebras and quantum groups, Mathematical Surveys and Monographs, vol. 150, American Mathematical Society, Providence, RI, 2008. MR 2457938, DOI 10.1090/surv/150
- Harm Derksen and Jerzy Weyman, An introduction to quiver representations, Graduate Studies in Mathematics, vol. 184, American Mathematical Society, Providence, RI, 2017. MR 3727119, DOI 10.1090/gsm/184
- Alexandru Dimca, Sheaves in topology, Universitext, Springer-Verlag, Berlin, 2004. MR 2050072, DOI 10.1007/978-3-642-18868-8
- Vladimir Drinfeld, On a conjecture of Kashiwara, Math. Res. Lett. 8 (2001), no. 5-6, 713–728. MR 1879815, DOI 10.4310/MRL.2001.v8.n6.a3
- V. Drinfeld and D. Gaitsgory, On a theorem of Braden, Transform. Groups 19 (2014), no. 2, 313–358. MR 3200429, DOI 10.1007/s00031-014-9267-8
- Bjørn Ian Dundas, A short course in differential topology, Cambridge Mathematical Textbooks, Cambridge University Press, Cambridge, 2018. MR 3793640, DOI 10.1017/9781108349130
- Charles Ehresmann, Les connexions infinitésimales dans un espace fibré différentiable, Colloque de topologie (espaces fibrés), Bruxelles, 1950, Georges Thone, Liège; Masson & Cie, Paris, 1951, pp. 29–55 (French). MR 0042768
- David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR 1322960, DOI 10.1007/978-1-4612-5350-1
- Ben Elias and Geordie Williamson, Soergel calculus, Represent. Theory 20 (2016), 295–374. MR 3555156, DOI 10.1090/ert/481
- Peter Fiebig, An upper bound on the exceptional characteristics for Lusztig’s character formula, J. Reine Angew. Math. 673 (2012), 1–31. MR 2999126, DOI 10.1515/CRELLE.2011.170
- Eberhard Freitag and Reinhardt Kiehl, Étale cohomology and the Weil conjecture, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 13, Springer-Verlag, Berlin, 1988. Translated from the German by Betty S. Waterhouse and William C. Waterhouse; With an historical introduction by J. A. Dieudonné. MR 926276, DOI 10.1007/978-3-662-02541-3
- Peter Freyd, Abelian categories. An introduction to the theory of functors, Harper’s Series in Modern Mathematics, Harper & Row, Publishers, New York, 1964. MR 0166240
- Michael D. Fried and Moshe Jarden, Field arithmetic, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 11, Springer-Verlag, Berlin, 2008. Revised by Jarden. MR 2445111
- Peter Gabriel, Unzerlegbare Darstellungen. I, Manuscripta Math. 6 (1972), 71–103; correction, ibid. 6 (1972), 309 (German, with English summary). MR 332887, DOI 10.1007/BF01298413
- Pierre Gabriel, Des catégories abéliennes, Bull. Soc. Math. France 90 (1962), 323–448 (French). MR 232821
- D. Gaitsgory, On de Jong’s conjecture, Israel J. Math. 157 (2007), 155–191. MR 2342444, DOI 10.1007/s11856-006-0006-2
- Sergei I. Gelfand and Yuri I. Manin, Methods of homological algebra, Springer-Verlag, Berlin, 1996. Translated from the 1988 Russian original. MR 1438306, DOI 10.1007/978-3-662-03220-6
- V. Ginzburg, Perverse sheaves on a loop group and Langlands’ duality, arXiv:alg-geom/9511007.
- Claude Godbillon, Éléments de topologie algébrique, Hermann, Paris, 1971 (French). MR 0301725
- Roger Godement, Topologie algébrique et théorie des faisceaux, Publ. Inst. Math. Univ. Strasbourg. No. 13, Hermann, Paris, 1958 (French). MR 0102797
- Mark Goresky and Robert MacPherson, Intersection homology theory, Topology 19 (1980), no. 2, 135–162. MR 572580, DOI 10.1016/0040-9383(80)90003-8
- Mark Goresky and Robert MacPherson, Intersection homology. II, Invent. Math. 72 (1983), no. 1, 77–129. MR 696691, DOI 10.1007/BF01389130
- Mark Goresky and Robert MacPherson, Morse theory and intersection homology theory, Analysis and topology on singular spaces, II, III (Luminy, 1981) Astérisque, vol. 101, Soc. Math. France, Paris, 1983, pp. 135–192. MR 737930
- Mark Goresky and Robert MacPherson, Stratified Morse theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 14, Springer-Verlag, Berlin, 1988. MR 932724, DOI 10.1007/978-3-642-71714-7
- Mark Goresky and Robert MacPherson, Local contribution to the Lefschetz fixed point formula, Invent. Math. 111 (1993), no. 1, 1–33. MR 1193595, DOI 10.1007/BF01231277
- Phillip A. Griffiths, On the periods of integrals on algebraic manifolds, Rice Univ. Stud. 54 (1968), no. 4, 21–38. MR 242844
- A. Grothendieck, Éléments de géométrie algébrique. II. Étude globale élémentaire de quelques classes de morphismes, Inst. Hautes Études Sci. Publ. Math. 8 (1961), 222 (French). MR 217084
- A. Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. II, Inst. Hautes Études Sci. Publ. Math. 24 (1965), 231 (French). MR 199181
- A. Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas IV, Inst. Hautes Études Sci. Publ. Math. 32 (1967), 361 (French). MR 238860
- Rajendra V. Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Deformations of $\Bbb A^1$-fibrations, Automorphisms in birational and affine geometry, Springer Proc. Math. Stat., vol. 79, Springer, Cham, 2014, pp. 327–361. MR 3229360, DOI 10.1007/978-3-319-05681-4_{1}9
- H. C. Hansen, On cycles in flag manifolds, Math. Scand. 33 (1973), 269–274 (1974). MR 376703, DOI 10.7146/math.scand.a-11489
- Robin Hartshorne, Residues and duality, Lecture Notes in Mathematics, No. 20, Springer-Verlag, Berlin-New York, 1966. Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64; With an appendix by P. Deligne. MR 0222093
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
- Allen Hatcher, Algebraic topology, Cambridge University Press, Cambridge, 2002. MR 1867354
- Joachim Hilgert and Karl-Hermann Neeb, Structure and geometry of Lie groups, Springer Monographs in Mathematics, Springer, New York, 2012. MR 3025417, DOI 10.1007/978-0-387-84794-8
- Heisuke Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109–203; ibid. (2) 79 (1964), 205–326. MR 0199184, DOI 10.2307/1970547
- Heisuke Hironaka, Triangulations of algebraic sets, Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974) Amer. Math. Soc., Providence, R.I., 1975, pp. 165–185. MR 0374131
- Chung Wu Ho, A note on proper maps, Proc. Amer. Math. Soc. 51 (1975), 237–241. MR 370471, DOI 10.1090/S0002-9939-1975-0370471-3
- Jin Hong and Seok-Jin Kang, Introduction to quantum groups and crystal bases, Graduate Studies in Mathematics, vol. 42, American Mathematical Society, Providence, RI, 2002. MR 1881971, DOI 10.1090/gsm/042
- Ryoshi Hotta, On Springer’s representations, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), no. 3, 863–876 (1982). MR 656061
- R. Hotta and T. A. Springer, A specialization theorem for certain Weyl group representations and an application to the Green polynomials of unitary groups, Invent. Math. 41 (1977), no. 2, 113–127. MR 486164, DOI 10.1007/BF01418371
- Ryoshi Hotta, Kiyoshi Takeuchi, and Toshiyuki Tanisaki, $D$-modules, perverse sheaves, and representation theory, Progress in Mathematics, vol. 236, Birkhäuser Boston, Inc., Boston, MA, 2008. Translated from the 1995 Japanese edition by Takeuchi. MR 2357361, DOI 10.1007/978-0-8176-4523-6
- Christian Houzel, Histoire de la théorie des faisceaux, Gaz. Math. 84, suppl. (2000), 35–52 (French). Jean Leray (1906–1998). MR 1775588
- James E. Humphreys, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics, vol. 29, Cambridge University Press, Cambridge, 1990. MR 1066460, DOI 10.1017/CBO9780511623646
- Luc Illusie, Autour du théorème de monodromie locale, Astérisque 223 (1994), 9–57 (French). Périodes $p$-adiques (Bures-sur-Yvette, 1988). MR 1293970
- Nagayoshi Iwahori, On the structure of a Hecke ring of a Chevalley group over a finite field, J. Fac. Sci. Univ. Tokyo Sect. I 10 (1964), 215–236 (1964). MR 165016
- N. Iwahori and H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke rings of ${\mathfrak {p}}$-adic Chevalley groups, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 5–48. MR 185016
- Nathan Jacobson, Completely reducible Lie algebras of linear transformations, Proc. Amer. Math. Soc. 2 (1951), 105–113. MR 49882, DOI 10.1090/S0002-9939-1951-0049882-5
- I. M. James, The topology of Stiefel manifolds, London Mathematical Society Lecture Note Series, No. 24, Cambridge University Press, Cambridge-New York-Melbourne, 1976. MR 0431239
- Jens Carsten Jantzen, Representations of algebraic groups, 2nd ed., Mathematical Surveys and Monographs, vol. 107, American Mathematical Society, Providence, RI, 2003. MR 2015057
- D. Juteau, Modular representations of reductive groups and geometry of affine Grassmannians, arXiv:0804.2041.
- —, Modular Springer correspondence, decomposition matrices, and basic sets, arXiv:1410.1471.
- —, Modular Springer correspondence and decomposition matrices, Ph.D. thesis, Université Paris 7, 2007.
- Daniel Juteau, Decomposition numbers for perverse sheaves, Ann. Inst. Fourier (Grenoble) 59 (2009), no. 3, 1177–1229 (English, with English and French summaries). MR 2543666
- D. Juteau, C. Lecouvey, and K. Sorlin, Springer basic sets and modular Springer correspondence for classical types, arXiv:1410.1477.
- Daniel Juteau, Carl Mautner, and Geordie Williamson, Parity sheaves, J. Amer. Math. Soc. 27 (2014), no. 4, 1169–1212. MR 3230821, DOI 10.1090/S0894-0347-2014-00804-3
- Masaki Kashiwara, The Riemann-Hilbert problem for holonomic systems, Publ. Res. Inst. Math. Sci. 20 (1984), no. 2, 319–365. MR 743382, DOI 10.2977/prims/1195181610
- M. Kashiwara, On crystal bases of the $Q$-analogue of universal enveloping algebras, Duke Math. J. 63 (1991), no. 2, 465–516. MR 1115118, DOI 10.1215/S0012-7094-91-06321-0
- Masaki Kashiwara, Semisimple holonomic $\scr D$-modules, Topological field theory, primitive forms and related topics (Kyoto, 1996) Progr. Math., vol. 160, Birkhäuser Boston, Boston, MA, 1998, pp. 267–271. MR 1653028
- Masaki Kashiwara, $D$-modules and microlocal calculus, Translations of Mathematical Monographs, vol. 217, American Mathematical Society, Providence, RI, 2003. Translated from the 2000 Japanese original by Mutsumi Saito; Iwanami Series in Modern Mathematics. MR 1943036, DOI 10.1090/mmono/217
- Masaki Kashiwara and Pierre Schapira, Sheaves on manifolds, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 292, Springer-Verlag, Berlin, 1994. With a chapter in French by Christian Houzel; Corrected reprint of the 1990 original. MR 1299726
- Masaki Kashiwara and Pierre Schapira, Categories and sheaves, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 332, Springer-Verlag, Berlin, 2006. MR 2182076, DOI 10.1007/3-540-27950-4
- Masaki Kashiwara and Toshiyuki Tanisaki, Kazhdan-Lusztig conjecture for affine Lie algebras with negative level, Duke Math. J. 77 (1995), no. 1, 21–62. MR 1317626, DOI 10.1215/S0012-7094-95-07702-3
- Shin-ichi Kato, Spherical functions and a $q$-analogue of Kostant’s weight multiplicity formula, Invent. Math. 66 (1982), no. 3, 461–468. MR 662602, DOI 10.1007/BF01389223
- David Kazhdan and George Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), no. 2, 165–184. MR 560412, DOI 10.1007/BF01390031
- David Kazhdan and George Lusztig, Schubert varieties and Poincaré duality, Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979) Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., 1980, pp. 185–203. MR 573434
- David Kazhdan and George Lusztig, Affine Lie algebras and quantum groups, Internat. Math. Res. Notices 2 (1991), 21–29. MR 1104840, DOI 10.1155/S1073792891000041
- G. M. Kelly, On MacLane’s conditions for coherence of natural associativities, commutativities, etc, J. Algebra 1 (1964), 397–402. MR 182649, DOI 10.1016/0021-8693(64)90018-3
- G. M. Kelly and M. L. Laplaza, Coherence for compact closed categories, J. Pure Appl. Algebra 19 (1980), 193–213. MR 593254, DOI 10.1016/0022-4049(80)90101-2
- Mikhail Khovanov and Aaron D. Lauda, A diagrammatic approach to categorification of quantum groups. I, Represent. Theory 13 (2009), 309–347. MR 2525917, DOI 10.1090/S1088-4165-09-00346-X
- Mikhail Khovanov and Aaron D. Lauda, A diagrammatic approach to categorification of quantum groups II, Trans. Amer. Math. Soc. 363 (2011), no. 5, 2685–2700. MR 2763732, DOI 10.1090/S0002-9947-2010-05210-9
- Reinhardt Kiehl and Rainer Weissauer, Weil conjectures, perverse sheaves and $l$’adic Fourier transform, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 42, Springer-Verlag, Berlin, 2001. MR 1855066, DOI 10.1007/978-3-662-04576-3
- Frances Kirwan, Intersection homology and torus actions, J. Amer. Math. Soc. 1 (1988), no. 2, 385–400. MR 928263, DOI 10.1090/S0894-0347-1988-0928263-7
- Steven L. Kleiman, The development of intersection homology theory, Pure Appl. Math. Q. 3 (2007), no. 1, Special Issue: In honor of Robert D. MacPherson., 225–282. MR 2330160, DOI 10.4310/PAMQ.2007.v3.n1.a8
- Bertram Kostant, The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math. 81 (1959), 973–1032. MR 114875, DOI 10.2307/2372999
- Bertram Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327–404. MR 158024, DOI 10.2307/2373130
- Emmanuel Kowalski, An introduction to the representation theory of groups, Graduate Studies in Mathematics, vol. 155, American Mathematical Society, Providence, RI, 2014. MR 3236265, DOI 10.1090/gsm/155
- Henning Krause, Krull-Schmidt categories and projective covers, Expo. Math. 33 (2015), no. 4, 535–549. MR 3431480, DOI 10.1016/j.exmath.2015.10.001
- Shrawan Kumar, Kac-Moody groups, their flag varieties and representation theory, Progress in Mathematics, vol. 204, Birkhäuser Boston, Inc., Boston, MA, 2002. MR 1923198, DOI 10.1007/978-1-4612-0105-2
- T. Y. Lam, A first course in noncommutative rings, Graduate Texts in Mathematics, vol. 131, Springer-Verlag, New York, 1991. MR 1125071, DOI 10.1007/978-1-4684-0406-7
- T. Y. Lam, Lectures on modules and rings, Graduate Texts in Mathematics, vol. 189, Springer-Verlag, New York, 1999. MR 1653294, DOI 10.1007/978-1-4612-0525-8
- Yves Laszlo and Martin Olsson, The six operations for sheaves on Artin stacks. I. Finite coefficients, Publ. Math. Inst. Hautes Études Sci. 107 (2008), 109–168. MR 2434692, DOI 10.1007/s10240-008-0011-6
- Yves Laszlo and Martin Olsson, The six operations for sheaves on Artin stacks. II. Adic coefficients, Publ. Math. Inst. Hautes Études Sci. 107 (2008), 169–210. MR 2434693, DOI 10.1007/s10240-008-0012-5
- Yves Laszlo and Martin Olsson, Perverse $t$-structure on Artin stacks, Math. Z. 261 (2009), no. 4, 737–748. MR 2480756, DOI 10.1007/s00209-008-0348-z
- G. Laumon, Transformation de Fourier, constantes d’équations fonctionnelles et conjecture de Weil, Inst. Hautes Études Sci. Publ. Math. 65 (1987), 131–210 (French). MR 908218
- Gérard Laumon, Transformation de Fourier homogène, Bull. Soc. Math. France 131 (2003), no. 4, 527–551 (French, with English and French summaries). MR 2044494, DOI 10.24033/bsmf.2454
- Robert Lazarsfeld, Positivity in algebraic geometry. I, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 48, Springer-Verlag, Berlin, 2004. Classical setting: line bundles and linear series. MR 2095471, DOI 10.1007/978-3-642-18808-4
- Lê Dũng Tráng, Some remarks on relative monodromy, Real and complex singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976) Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, pp. 397–403. MR 0476739
- Jue Le and Xiao-Wu Chen, Karoubianness of a triangulated category, J. Algebra 310 (2007), no. 1, 452–457. MR 2307804, DOI 10.1016/j.jalgebra.2006.11.027
- Qing Liu, Algebraic geometry and arithmetic curves, Oxford Graduate Texts in Mathematics, vol. 6, Oxford University Press, Oxford, 2002. Translated from the French by Reinie Erné; Oxford Science Publications. MR 1917232
- George Lusztig, Character sheaves. I, Adv. in Math. 56 (1985), no. 3, 193–237. MR 792706, DOI 10.1016/0001-8708(85)90034-9
- George Lusztig, Some problems in the representation theory of finite Chevalley groups, The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979) Proc. Sympos. Pure Math., vol. 37, Amer. Math. Soc., Providence, R.I., 1980, pp. 313–317. MR 604598
- G. Lusztig, Green polynomials and singularities of unipotent classes, Adv. in Math. 42 (1981), no. 2, 169–178. MR 641425, DOI 10.1016/0001-8708(81)90038-4
- George Lusztig, Singularities, character formulas, and a $q$-analog of weight multiplicities, Analysis and topology on singular spaces, II, III (Luminy, 1981) Astérisque, vol. 101, Soc. Math. France, Paris, 1983, pp. 208–229. MR 737932
- G. Lusztig, Intersection cohomology complexes on a reductive group, Invent. Math. 75 (1984), no. 2, 205–272. MR 732546, DOI 10.1007/BF01388564
- George Lusztig, Fourier transforms on a semisimple Lie algebra over $\textbf {F}_q$, Algebraic groups Utrecht 1986, Lecture Notes in Math., vol. 1271, Springer, Berlin, 1987, pp. 177–188. MR 911139, DOI 10.1007/BFb0079237
- G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), no. 2, 447–498. MR 1035415, DOI 10.1090/S0894-0347-1990-1035415-6
- George Lusztig, Quantum groups at roots of $1$, Geom. Dedicata 35 (1990), no. 1-3, 89–113. MR 1066560, DOI 10.1007/BF00147341
- W. Lütkebohmert, On compactification of schemes, Manuscripta Math. 80 (1993), no. 1, 95–111. MR 1226600, DOI 10.1007/BF03026540
- Saunders Mac Lane, Categories for the working mathematician, 2nd ed., Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1998. MR 1712872
- I. G. Macdonald, Spherical functions on a group of $p$-adic type, Publications of the Ramanujan Institute, No. 2, University of Madras, Centre for Advanced Study in Mathematics, Ramanujan Institute, Madras, 1971. MR 0435301
- Robert MacPherson and Kari Vilonen, Elementary construction of perverse sheaves, Invent. Math. 84 (1986), no. 2, 403–435. MR 833195, DOI 10.1007/BF01388812
- A. Malcev, On semi-simple subgroups of Lie groups, Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR] 8 (1944), 143–174 (Russian, with English summary). MR 0011303
- J. G. M. Mars and T. A. Springer, Hecke algebra representations related to spherical varieties, Represent. Theory 2 (1998), 33–69. MR 1600804, DOI 10.1090/S1088-4165-98-00027-2
- David Massey, Natural commuting of vanishing cycles and the Verdier dual, Pacific J. Math. 284 (2016), no. 2, 431–437. MR 3544308, DOI 10.2140/pjm.2016.284.431
- John Mather, Notes on topological stability, Bull. Amer. Math. Soc. (N.S.) 49 (2012), no. 4, 475–506. MR 2958928, DOI 10.1090/S0273-0979-2012-01383-6
- Hideya Matsumoto, Analyse harmonique dans les systèmes de Tits bornologiques de type affine, Lecture Notes in Mathematics, Vol. 590, Springer-Verlag, Berlin-New York, 1977 (French). MR 0579177
- Hideyuki Matsumura, Commutative ring theory, 2nd ed., Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, Cambridge, 1989. Translated from the Japanese by M. Reid. MR 1011461
- Carl Mautner and Simon Riche, Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirković-Vilonen conjecture, J. Eur. Math. Soc. (JEMS) 20 (2018), no. 9, 2259–2332. MR 3836847, DOI 10.4171/JEMS/812
- J. P. May, The additivity of traces in triangulated categories, Adv. Math. 163 (2001), no. 1, 34–73. MR 1867203, DOI 10.1006/aima.2001.1995
- Z. Mebkhout, Une autre équivalence de catégories, Compositio Math. 51 (1984), no. 1, 63–88 (French). MR 734785
- John Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies, No. 61, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. MR 0239612
- I. Mirković, Character sheaves on reductive Lie algebras, Mosc. Math. J. 4 (2004), no. 4, 897–910, 981 (English, with English and Russian summaries). MR 2124171, DOI 10.17323/1609-4514-2004-4-4-897-910
- Ivan Mirković and Kari Vilonen, Perverse sheaves on affine Grassmannians and Langlands duality, Math. Res. Lett. 7 (2000), no. 1, 13–24. MR 1748284, DOI 10.4310/MRL.2000.v7.n1.a2
- I. Mirković and K. Vilonen, Geometric Langlands duality and representations of algebraic groups over commutative rings, Ann. of Math. (2) 166 (2007), no. 1, 95–143. MR 2342692, DOI 10.4007/annals.2007.166.95
- Takuro Mochizuki, Asymptotic behaviour of tame harmonic bundles and an application to pure twistor $D$-modules. I, Mem. Amer. Math. Soc. 185 (2007), no. 869, xii+324. MR 2281877, DOI 10.1090/memo/0869
- Takuro Mochizuki, Asymptotic behaviour of tame harmonic bundles and an application to pure twistor $D$-modules. II, Mem. Amer. Math. Soc. 185 (2007), no. 870, xii+565. MR 2283665, DOI 10.1090/memo/0870
- V. V. Morozov, On a nilpotent element in a semi-simple Lie algebra, C. R. (Doklady) Acad. Sci. URSS (N.S.) 36 (1942), 83–86. MR 0007750
- David Mumford, The red book of varieties and schemes, Second, expanded edition, Lecture Notes in Mathematics, vol. 1358, Springer-Verlag, Berlin, 1999. Includes the Michigan lectures (1974) on curves and their Jacobians; With contributions by Enrico Arbarello. MR 1748380, DOI 10.1007/b62130
- D. Mumford, J. Fogarty, and F. Kirwan, Geometric invariant theory, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas (2)], vol. 34, Springer-Verlag, Berlin, 1994. MR 1304906, DOI 10.1007/978-3-642-57916-5
- James R. Munkres, Elements of algebraic topology, Addison-Wesley Publishing Company, Menlo Park, CA, 1984. MR 755006
- Amnon Neeman, Triangulated categories, Annals of Mathematics Studies, vol. 148, Princeton University Press, Princeton, NJ, 2001. MR 1812507, DOI 10.1515/9781400837212
- Madhav V. Nori, Constructible sheaves, Algebra, arithmetic and geometry, Part I, II (Mumbai, 2000) Tata Inst. Fund. Res. Stud. Math., vol. 16, Tata Inst. Fund. Res., Bombay, 2002, pp. 471–491. MR 1940678
- Chris A. M. Peters and Joseph H. M. Steenbrink, Mixed Hodge structures, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 52, Springer-Verlag, Berlin, 2008. MR 2393625
- S. Ramanan, Global calculus, Graduate Studies in Mathematics, vol. 65, American Mathematical Society, Providence, RI, 2005. MR 2104612, DOI 10.1090/gsm/065
- Michel Raynaud, Faisceaux amples sur les schémas en groupes et les espaces homogènes, Lecture Notes in Mathematics, Vol. 119, Springer-Verlag, Berlin-New York, 1970 (French). MR 0260758
- Ryan Reich, Notes on Beilinson’s “How to glue perverse sheaves” [MR0923134], J. Singul. 1 (2010), 94–115. MR 2671769
- Ryan Cohen Reich, Obvious natural morphisms of sheaves are unique, Theory Appl. Categ. 29 (2014), No. 4, 48–99. MR 3192770
- S. Riche and G. Williamson, Smith–Treumann theory and the linkage principle, arXiv:2003.08522.
- Simon Riche and Geordie Williamson, Tilting modules and the $p$-canonical basis, Astérisque 397 (2018), ix+184 (English, with English and French summaries). MR 3805034
- Claus Michael Ringel, Hall algebras, Topics in algebra, Part 1 (Warsaw, 1988) Banach Center Publ., vol. 26, PWN, Warsaw, 1990, pp. 433–447. MR 1171248
- Claus Michael Ringel, Hall algebras and quantum groups, Invent. Math. 101 (1990), no. 3, 583–591. MR 1062796, DOI 10.1007/BF01231516
- Raphaël Rouquier, Quiver Hecke algebras and 2-Lie algebras, Algebra Colloq. 19 (2012), no. 2, 359–410. MR 2908731, DOI 10.1142/S1005386712000247
- Claude Sabbah, Polarizable twistor $\scr D$-modules, Astérisque 300 (2005), vi+208 (English, with English and French summaries). MR 2156523
- Morihiko Saito, Modules de Hodge polarisables, Publ. Res. Inst. Math. Sci. 24 (1988), no. 6, 849–995 (1989) (French). MR 1000123, DOI 10.2977/prims/1195173930
- Morihiko Saito, Extension of mixed Hodge modules, Compositio Math. 74 (1990), no. 2, 209–234. MR 1047741
- Morihiko Saito, Mixed Hodge modules, Publ. Res. Inst. Math. Sci. 26 (1990), no. 2, 221–333. MR 1047415, DOI 10.2977/prims/1195171082
- Ichirô Satake, Theory of spherical functions on reductive algebraic groups over ${\mathfrak {p}}$-adic fields, Inst. Hautes Études Sci. Publ. Math. 18 (1963), 5–69. MR 195863
- Ralf Schiffler, Quiver representations, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer, Cham, 2014. MR 3308668, DOI 10.1007/978-3-319-09204-1
- Wilfried Schmid, Variation of Hodge structure: the singularities of the period mapping, Invent. Math. 22 (1973), 211–319. MR 382272, DOI 10.1007/BF01389674
- J.-P. Schneiders, Introduction to characteristic classes and index theory, Textos de Matemática, no. 13, Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, 2000.
- Jörg Schürmann, Topology of singular spaces and constructible sheaves, Instytut Matematyczny Polskiej Akademii Nauk. Monografie Matematyczne (New Series) [Mathematics Institute of the Polish Academy of Sciences. Mathematical Monographs (New Series)], vol. 63, Birkhäuser Verlag, Basel, 2003. MR 2031639, DOI 10.1007/978-3-0348-8061-9
- Y. Sella, Comparison of sheaf cohomology and singular cohomology, arXiv:1602.06674.
- J.-P. Serre, Espaces fibrés algébriques, Séminaire C. Chevalley; 2e année: 1958. Anneaux de Chow et applications, Secrétariat mathématique, Paris, 1958, pp. 1–37.
- Jean-Pierre Serre, Local fields, Graduate Texts in Mathematics, vol. 67, Springer-Verlag, New York-Berlin, 1979. Translated from the French by Marvin Jay Greenberg. MR 554237
- Igor R. Shafarevich, Basic algebraic geometry. 1, Translated from the 2007 third Russian edition, Springer, Heidelberg, 2013. Varieties in projective space. MR 3100243
- Igor R. Shafarevich, Basic algebraic geometry. 2, 3rd ed., Springer, Heidelberg, 2013. Schemes and complex manifolds; Translated from the 2007 third Russian edition by Miles Reid. MR 3100288
- Toshiaki Shoji, On the Springer representations of the Weyl groups of classical algebraic groups, Comm. Algebra 7 (1979), no. 16, 1713–1745. MR 546195, DOI 10.1080/00927877908822425
- Toshiaki Shoji, On the Springer representations of Chevalley groups of type $F_{4}$, Comm. Algebra 8 (1980), no. 5, 409–440. MR 561538, DOI 10.1080/00927878008822466
- Toshiaki Shoji, Geometry of orbits and Springer correspondence, Astérisque 168 (1988), 9, 61–140. Orbites unipotentes et représentations, I. MR 1021493
- Peter Slodowy, Four lectures on simple groups and singularities, Communications of the Mathematical Institute, Rijksuniversiteit Utrecht, vol. 11, Rijksuniversiteit Utrecht, Mathematical Institute, Utrecht, 1980. MR 563725
- Peter Slodowy, Simple singularities and simple algebraic groups, Lecture Notes in Mathematics, vol. 815, Springer, Berlin, 1980. MR 584445
- Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen, and William Traves, An invitation to algebraic geometry, Universitext, Springer-Verlag, New York, 2000. MR 1788561, DOI 10.1007/978-1-4757-4497-2
- Wolfgang Soergel, Kategorie $\scr O$, perverse Garben und Moduln über den Koinvarianten zur Weylgruppe, J. Amer. Math. Soc. 3 (1990), no. 2, 421–445 (German, with English summary). MR 1029692, DOI 10.1090/S0894-0347-1990-1029692-5
- Wolfgang Soergel, The combinatorics of Harish-Chandra bimodules, J. Reine Angew. Math. 429 (1992), 49–74. MR 1173115, DOI 10.1515/crll.1992.429.49
- Wolfgang Soergel, Kazhdan-Lusztig polynomials and a combinatoric[s] for tilting modules, Represent. Theory 1 (1997), 83–114. MR 1444322, DOI 10.1090/S1088-4165-97-00021-6
- Wolfgang Soergel, On the relation between intersection cohomology and representation theory in positive characteristic, J. Pure Appl. Algebra 152 (2000), no. 1-3, 311–335. Commutative algebra, homological algebra and representation theory (Catania/Genoa/Rome, 1998). MR 1784005, DOI 10.1016/S0022-4049(99)00138-3
- Wolfgang Soergel, Kazhdan-Lusztig-Polynome und unzerlegbare Bimoduln über Polynomringen, J. Inst. Math. Jussieu 6 (2007), no. 3, 501–525 (German, with English and German summaries). MR 2329762, DOI 10.1017/S1474748007000023
- N. Spaltenstein, Resolutions of unbounded complexes, Compositio Math. 65 (1988), no. 2, 121–154. MR 932640
- Nicolas Spaltenstein, Classes unipotentes et sous-groupes de Borel, Lecture Notes in Mathematics, vol. 946, Springer-Verlag, Berlin-New York, 1982 (French). MR 672610
- Edwin H. Spanier, Algebraic topology, Springer-Verlag, New York, [1995?]. Corrected reprint of the 1966 original. MR 1325242
- T. A. Springer, Trigonometric sums, Green functions of finite groups and representations of Weyl groups, Invent. Math. 36 (1976), 173–207. MR 442103, DOI 10.1007/BF01390009
- T. A. Springer, A construction of representations of Weyl groups, Invent. Math. 44 (1978), no. 3, 279–293. MR 491988, DOI 10.1007/BF01403165
- T. A. Springer, Quelques applications de la cohomologie d’intersection, Bourbaki Seminar, Vol. 1981/1982, Astérisque, vol. 92, Soc. Math. France, Paris, 1982, pp. 249–273 (French). MR 689533
- T. A. Springer, A purity result for fixed point varieties in flag manifolds, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 31 (1984), no. 2, 271–282. MR 763421
- T. A. Springer, Linear algebraic groups, 2nd ed., Progress in Mathematics, vol. 9, Birkhäuser Boston, Inc., Boston, MA, 1998. MR 1642713, DOI 10.1007/978-0-8176-4840-4
- T. A. Springer and R. Steinberg, Conjugacy classes, Seminar on Algebraic Groups and Related Finite Groups (The Institute for Advanced Study, Princeton, N.J., 1968/69) Lecture Notes in Mathematics, Vol. 131, Springer, Berlin, 1970, pp. 167–266. MR 0268192
- N. E. Steenrod, Homology with local coefficients, Ann. of Math. (2) 44 (1943), 610–627. MR 9114, DOI 10.2307/1969099
- Robert Steinberg, On the desingularization of the unipotent variety, Invent. Math. 36 (1976), 209–224. MR 430094, DOI 10.1007/BF01390010
- Hideyasu Sumihiro, Equivariant completion, J. Math. Kyoto Univ. 14 (1974), 1–28. MR 337963, DOI 10.1215/kjm/1250523277
- Shenghao Sun, Generic base change, Artin’s comparison theorem, and the decomposition theorem for complex Artin stacks, J. Algebraic Geom. 26 (2017), no. 3, 513–555. MR 3647792, DOI 10.1090/jag/683
- R. Thom, Ensembles et morphismes stratifiés, Bull. Amer. Math. Soc. 75 (1969), 240–284 (French). MR 239613, DOI 10.1090/S0002-9904-1969-12138-5
- M. Varagnolo and E. Vasserot, Canonical bases and KLR-algebras, J. Reine Angew. Math. 659 (2011), 67–100. MR 2837011, DOI 10.1515/CRELLE.2011.068
- Jean-Louis Verdier, Dualité dans la cohomologie des espaces localement compacts, Séminaire Bourbaki, Vol. 9, Soc. Math. France, Paris, 1995, pp. Exp. No. 300, 337–349 (French). MR 1610971
- Jean-Louis Verdier, Classe d’homologie associée à un cycle, Séminaire de géométrie analytique (École Norm. Sup., Paris, 1974–75) Astérisque, No. 36-37, Soc. Math. France, Paris, 1976, pp. 101–151 (French). MR 0447623
- Jean-Louis Verdier, Extension of a perverse sheaf over a closed subspace, Astérisque 130 (1985), 210–217. Differential systems and singularities (Luminy, 1983). MR 804054
- Jean-Louis Verdier, Des catégories dérivées des catégories abéliennes, Astérisque 239 (1996), xii+253 pp. (1997) (French, with French summary). With a preface by Luc Illusie; Edited and with a note by Georges Maltsiniotis. MR 1453167
- Daya-Nand Verma, The rôle of affine Weyl groups in the representation theory of algebraic Chevalley groups and their Lie algebras, Lie groups and their representations (Proc. Summer School, Bolyai János Math. Soc., Budapest, 1971) Halsted, New York, 1975, pp. 653–705. MR 0409673
- Hassler Whitney, Local properties of analytic varieties, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, pp. 205–244. MR 0188486
- Geordie Williamson, On torsion in the intersection cohomology of Schubert varieties, J. Algebra 475 (2017), 207–228. MR 3612469, DOI 10.1016/j.jalgebra.2016.06.006
- Geordie Williamson, Schubert calculus and torsion explosion, J. Amer. Math. Soc. 30 (2017), no. 4, 1023–1046. With a joint appendix with Alex Kontorovich and Peter J. McNamara. MR 3671935, DOI 10.1090/jams/868