Ramification of higher local fields, approaches and questions
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- by L. Xiao and I. Zhukov
- St. Petersburg Math. J. 26 (2015), 695-740
- DOI: https://doi.org/10.1090/spmj/1355
- Published electronically: July 27, 2015
- PDF | Request permission
Abstract:
A survey paper that includes facts, ideas and problems related to ramification in finite extensions of complete discrete valuation fields with arbitrary residue fields. Some new results are included.References
- Ahmed Abbes and Abdellah Mokrane, Sous-groupes canoniques et cycles évanescents $p$-adiques pour les variétés abéliennes, Publ. Math. Inst. Hautes Études Sci. 99 (2004), 117–162 (French). MR 2075884, DOI 10.1007/s10240-004-0022-x
- Ahmed Abbes and Takeshi Saito, Ramification of local fields with imperfect residue fields, Amer. J. Math. 124 (2002), no. 5, 879–920. MR 1925338
- Ahmed Abbes and Takeshi Saito, Ramification of local fields with imperfect residue fields. II, Doc. Math. Extra Vol. (2003), 5–72. Kazuya Kato’s fiftieth birthday. MR 2046594
- Ahmed Abbes and Takeshi Saito, Analyse micro-locale $l$-adique en caractéristique $p>0$: le cas d’un trait, Publ. Res. Inst. Math. Sci. 45 (2009), no. 1, 25–74 (French, with English and French summaries). MR 2512777, DOI 10.2977/prims/1234361154
- Ahmed Abbes and Takeshi Saito, Ramification and cleanliness, Tohoku Math. J. (2) 63 (2011), no. 4, 775–853. MR 2872965, DOI 10.2748/tmj/1325886290
- Victor A. Abrashkin, On a local analogue of the Grothendieck conjecture, Internat. J. Math. 11 (2000), no. 2, 133–175. MR 1754618, DOI 10.1142/S0129167X0000009X
- Victor Abrashkin, Ramification theory for higher dimensional local fields, Algebraic number theory and algebraic geometry, Contemp. Math., vol. 300, Amer. Math. Soc., Providence, RI, 2002, pp. 1–16. MR 1936364, DOI 10.1090/conm/300/05140
- V. A. Abrashkin, An analogue of Grothendieck’s conjecture for two-dimensional local fields of finite characteristic, Tr. Mat. Inst. Steklova 241 (2003), no. Teor. Chisel, Algebra i Algebr. Geom., 8–42 (Russian, with Russian summary); English transl., Proc. Steklov Inst. Math. 2(241) (2003), 2–34. MR 2024042
- Victor Abrashkin, An analogue of the field-of-norms functor and of the Grothendieck conjecture, J. Algebraic Geom. 16 (2007), no. 4, 671–730. MR 2357687, DOI 10.1090/S1056-3911-07-00470-5
- Victor Abrashkin, Modified proof of a local analogue of the Grothendieck conjecture, J. Théor. Nombres Bordeaux 22 (2010), no. 1, 1–50 (English, with English and French summaries). MR 2675872
- I. Barrientos, Log ramification via curves in rank 1, Preprint, 2013, arXiv:1307.5814.
- Pierre Berthelot, Introduction à la théorie arithmétique des $\scr D$-modules, Astérisque 279 (2002), 1–80 (French, with French summary). Cohomologies $p$-adiques et applications arithmétiques, II. MR 1922828
- Robert Boltje, G.-Martin Cram, and V. P. Snaith, Conductors in the non-separable residue field case, Algebraic $K$-theory and algebraic topology (Lake Louise, AB, 1991) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 407, Kluwer Acad. Publ., Dordrecht, 1993, pp. 1–34. MR 1367290, DOI 10.1007/978-94-017-0695-7_{1}
- S. Bosch, U. Güntzer, and R. Remmert, Non-Archimedean analysis, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 261, Springer-Verlag, Berlin, 1984. A systematic approach to rigid analytic geometry. MR 746961, DOI 10.1007/978-3-642-52229-1
- Yousra Boubakri, Gert-Martin Greuel, and Thomas Markwig, Invariants of hypersurface singularities in positive characteristic, Rev. Mat. Complut. 25 (2012), no. 1, 61–85. MR 2876917, DOI 10.1007/s13163-010-0056-1
- J. M. Borger, Kato’s conductor and generic residual perfection, Preprint, 2002, arXiv:math/ 0112306.
- James M. Borger, Conductors and the moduli of residual perfection, Math. Ann. 329 (2004), no. 1, 1–30. MR 2052867, DOI 10.1007/s00208-003-0490-1
- Jean-Luc Brylinski, Théorie du corps de classes de Kato et revêtements abéliens de surfaces, Ann. Inst. Fourier (Grenoble) 33 (1983), no. 3, 23–38 (French, with English summary). MR 723946
- Bruno Chiarellotto and Andrea Pulita, Arithmetic and differential Swan conductors of rank one representations with finite local monodromy, Amer. J. Math. 131 (2009), no. 6, 1743–1794. MR 2567506, DOI 10.1353/ajm.0.0083
- Steven Dale Cutkosky and Olivier Piltant, Ramification of valuations, Adv. Math. 183 (2004), no. 1, 1–79. MR 2038546, DOI 10.1016/S0001-8708(03)00082-3
- A. Campillo and I. B. Zhukov, Curve singularities and ramification of surface morphisms. (to appear)
- P. Deligne, Letter to L. Illusie of 28.11.76. (unpublished)
- P. Deligne, Les corps locaux de caractéristique $p$, limites de corps locaux de caractéristique $0$, Representations of reductive groups over a local field, Travaux en Cours, Hermann, Paris, 1984, pp. 119–157 (French). MR 771673
- Bart de Smit, Ramification groups of local fields with imperfect residue class fields, J. Number Theory 44 (1993), no. 3, 229–236. MR 1233284, DOI 10.1006/jnth.1993.1048
- Helmut P. Epp, Eliminating wild ramification, Invent. Math. 19 (1973), 235–249. MR 321929, DOI 10.1007/BF01390208
- Hélène Esnault and Moritz Kerz, A finiteness theorem for Galois representations of function fields over finite fields (after Deligne), Acta Math. Vietnam. 37 (2012), no. 4, 531–562. MR 3058662
- I. N. Faizov, Ramification jump in model extensions of degree $p$, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 413 (2013), no. Voprosy Teorii Predstavleniĭ Algebr i Grupp. 24, 183–218, 231 (Russian, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 202 (2014), no. 3, 455–478. MR 3073065, DOI 10.1007/s10958-014-2055-0
- Ivan B. Fesenko, Abelian local $p$-class field theory, Math. Ann. 301 (1995), no. 3, 561–586. MR 1324527, DOI 10.1007/BF01446646
- Ivan B. Fesenko, Hasse-Arf property and abelian extensions, Math. Nachr. 174 (1995), 81–87. MR 1349039, DOI 10.1002/mana.19951740108
- Ivan B. Fesenko, Abelian extensions of complete discrete valuation fields, Number theory (Paris, 1993–1994) London Math. Soc. Lecture Note Ser., vol. 235, Cambridge Univ. Press, Cambridge, 1996, pp. 47–74. MR 1628793, DOI 10.1017/CBO9780511662003.003
- Ivan Fesenko, Nonabelian local reciprocity maps, Class field theory—its centenary and prospect (Tokyo, 1998) Adv. Stud. Pure Math., vol. 30, Math. Soc. Japan, Tokyo, 2001, pp. 63–78. MR 1846451, DOI 10.2969/aspm/03010063
- Ivan Fesenko, Analysis on arithmetic schemes. II, J. K-Theory 5 (2010), no. 3, 437–557. MR 2658047, DOI 10.1017/is010004028jkt103
- I. B. Fesenko and S. V. Vostokov, Local fields and their extensions, 2nd ed., Translations of Mathematical Monographs, vol. 121, American Mathematical Society, Providence, RI, 2002. With a foreword by I. R. Shafarevich. MR 1915966, DOI 10.1090/mmono/121
- Jean-Marc Fontaine and Jean-Pierre Wintenberger, Extensions algébrique et corps des normes des extensions APF des corps locaux, C. R. Acad. Sci. Paris Sér. A-B 288 (1979), no. 8, A441–A444 (French, with English summary). MR 527692
- Jean-Marc Fontaine and Jean-Pierre Wintenberger, Le “corps des normes” de certaines extensions algébriques de corps locaux, C. R. Acad. Sci. Paris Sér. A-B 288 (1979), no. 6, A367–A370 (French, with English summary). MR 526137
- Shin Hattori, Ramification correspondence of finite flat group schemes over equal and mixed characteristic local fields, J. Number Theory 132 (2012), no. 10, 2084–2102. MR 2944746, DOI 10.1016/j.jnt.2012.04.003
- Shin Hattori, On lower ramification subgroups and canonical subgroups, Algebra Number Theory 8 (2014), no. 2, 303–330. MR 3212858, DOI 10.2140/ant.2014.8.303
- Ivan Fesenko and Masato Kurihara (eds.), Invitation to higher local fields, Geometry & Topology Monographs, vol. 3, Geometry & Topology Publications, Coventry, 2000. Papers from the conference held in Münster, August 29–September 5, 1999. MR 1804915, DOI 10.2140/gtm.2000.3
- Toshiro Hiranouchi, Ramification of truncated discrete valuation rings: a survey, Algebraic number theory and related topics 2008, RIMS Kôkyûroku Bessatsu, B19, Res. Inst. Math. Sci. (RIMS), Kyoto, 2010, pp. 35–43. MR 2757556
- Toshiro Hiranouchi and Yuichiro Taguchi, Extensions of truncated discrete valuation rings, Pure Appl. Math. Q. 4 (2008), no. 4, Special Issue: In honor of Jean-Pierre Serre., 1205–1214. MR 2441698, DOI 10.4310/PAMQ.2008.v4.n4.a9
- 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
- Osamu Hyodo, Wild ramification in the imperfect residue field case, Galois representations and arithmetic algebraic geometry (Kyoto, 1985/Tokyo, 1986) Adv. Stud. Pure Math., vol. 12, North-Holland, Amsterdam, 1987, pp. 287–314. MR 948250, DOI 10.2969/aspm/01210287
- O. Yu. Ivanova, The rank of a topological $K$-group as a $\Bbb Z_p$-module, Algebra i Analiz 20 (2008), no. 4, 87–117 (Russian); English transl., St. Petersburg Math. J. 20 (2009), no. 4, 569–591. MR 2473745, DOI 10.1090/S1061-0022-09-01062-0
- O. Yu. Ivanova, On a connection between Kurihara’s classification and the theory of elimination of ramification, Algebra i Analiz 24 (2012), no. 2, 130–153 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 24 (2013), no. 2, 283–299. MR 3013329, DOI 10.1090/S1061-0022-2013-01239-8
- O. Yu. Ivanova, Kurihara’s classification and extensions of the maximal depth for multidimensional local fields, Algebra i Analiz 24 (2012), no. 6, 42–76 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 24 (2013), no. 6, 877–901. MR 3097553, DOI 10.1090/S1061-0022-2013-01271-4
- Kâzim Ilhan Ikeda and Erol Serbest, Ramification theory in non-abelian local class field theory, Acta Arith. 144 (2010), no. 4, 373–393. MR 2684288, DOI 10.4064/aa144-4-4
- Kazuya Kato, Vanishing cycles, ramification of valuations, and class field theory, Duke Math. J. 55 (1987), no. 3, 629–659. MR 904945, DOI 10.1215/S0012-7094-87-05532-3
- Kazuya Kato, Swan conductors for characters of degree one in the imperfect residue field case, Algebraic $K$-theory and algebraic number theory (Honolulu, HI, 1987) Contemp. Math., vol. 83, Amer. Math. Soc., Providence, RI, 1989, pp. 101–131. MR 991978, DOI 10.1090/conm/083/991978
- Kazuya Kato, Class field theory, ${\scr D}$-modules, and ramification on higher-dimensional schemes. I, Amer. J. Math. 116 (1994), no. 4, 757–784. MR 1287939, DOI 10.2307/2375001
- Kazuya Kato and Takeshi Saito, Ramification theory for varieties over a perfect field, Ann. of Math. (2) 168 (2008), no. 1, 33–96. MR 2415398, DOI 10.4007/annals.2008.168.33
- Kazuya Kato and Takeshi Saito, Ramification theory for varieties over a local field, Publ. Math. Inst. Hautes Études Sci. 117 (2013), 1–178. MR 3090259, DOI 10.1007/s10240-013-0048-z
- Nicholas M. Katz, Exponential sums and differential equations, Annals of Mathematics Studies, vol. 124, Princeton University Press, Princeton, NJ, 1990. MR 1081536, DOI 10.1515/9781400882434
- Kiran S. Kedlaya, Local monodromy of $p$-adic differential equations: an overview, Int. J. Number Theory 1 (2005), no. 1, 109–154. MR 2172335, DOI 10.1142/S179304210500008X
- Kiran S. Kedlaya, Fourier transforms and $p$-adic ‘Weil II’, Compos. Math. 142 (2006), no. 6, 1426–1450. MR 2278753, DOI 10.1112/S0010437X06002338
- Kiran S. Kedlaya, Swan conductors for $p$-adic differential modules. I. A local construction, Algebra Number Theory 1 (2007), no. 3, 269–300. MR 2361935, DOI 10.2140/ant.2007.1.269
- Kiran S. Kedlaya, $p$-adic differential equations, Cambridge Studies in Advanced Mathematics, vol. 125, Cambridge University Press, Cambridge, 2010. MR 2663480, DOI 10.1017/CBO9780511750922
- Kiran S. Kedlaya, Good formal structures for flat meromorphic connections, I: surfaces, Duke Math. J. 154 (2010), no. 2, 343–418. MR 2682186, DOI 10.1215/00127094-2010-041
- Kiran S. Kedlaya, Swan conductors for $p$-adic differential modules. II: global variation, J. Inst. Math. Jussieu 10 (2011), no. 1, 191–224. MR 2749575, DOI 10.1017/S1474748010000137
- Kiran S. Kedlaya, Good formal structures for flat meromorphic connections, II: excellent schemes, J. Amer. Math. Soc. 24 (2011), no. 1, 183–229. MR 2726603, DOI 10.1090/S0894-0347-2010-00681-9
- Kiran S. Kedlaya and Liang Xiao, Differential modules on $p$-adic polyannuli, J. Inst. Math. Jussieu 9 (2010), no. 1, 155–201. MR 2576801, DOI 10.1017/S1474748009000085
- Bernhard Köck, Computing the equivariant Euler characteristic of Zariski and étale sheaves on curves, Homology Homotopy Appl. 7 (2005), no. 3, 83–98. MR 2205171
- Franz-Viktor Kuhlmann, A correction to: “Elimination of wild ramification” [Invent. Math. 19 (1973), 235–249; MR0321929 (48 #294)] by H. P. Epp, Invent. Math. 153 (2003), no. 3, 679–681. MR 2000472, DOI 10.1007/s00222-003-0297-4
- Masato Kurihara, On two types of complete discrete valuation fields, Compositio Math. 63 (1987), no. 2, 237–257. MR 906373
- I. B. Zhukov and M. V. Koroteev, Elimination of wild ramification, Algebra i Analiz 11 (1999), no. 6, 153–177 (Russian); English transl., St. Petersburg Math. J. 11 (2000), no. 6, 1063–1083. MR 1746073
- G. Laumon, Semi-continuité du conducteur de Swan (d’après P. Deligne), The Euler-Poincaré characteristic (French), Astérisque, vol. 82, Soc. Math. France, Paris, 1981, pp. 173–219 (French). MR 629128
- V. G. Lomadze, On the ramification theory of two-dimensional local fields, Mat. Sb. (N.S.) 109(151) (1979), no. 3, 378–394, 478 (Russian). MR 542807
- A. Melle-Hernández and C. T. C. Wall, Pencils of curves on smooth surfaces, Proc. London Math. Soc. (3) 83 (2001), no. 2, 257–278. MR 1839454, DOI 10.1112/plms/83.2.257
- Hiroo Miki, On $Z_{p}$-extensions of complete $p$-adic power series fields and function fields, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 21 (1974), 377–393. MR 364206
- Hiroo Miki, On the ramification numbers of cyclic $p$-extensions over local fields, J. Reine Angew. Math. 328 (1981), 99–115. MR 636198, DOI 10.1515/crll.1981.328.99
- James S. Milne, Étale cohomology, Princeton Mathematical Series, No. 33, Princeton University Press, Princeton, N.J., 1980. MR 559531
- Shinichi Mochizuki, A version of the Grothendieck conjecture for $p$-adic local fields, Internat. J. Math. 8 (1997), no. 4, 499–506. MR 1460898, DOI 10.1142/S0129167X97000251
- Takuro Mochizuki, Wild harmonic bundles and wild pure twistor $D$-modules, Astérisque 340 (2011), x+607 (English, with English and French summaries). MR 2919903
- K. N. Ponomarëv, Solvable elimination of ramification in extensions of discretely valued fields, Algebra i Logika 37 (1998), no. 1, 63–87, 123 (Russian, with Russian summary); English transl., Algebra and Logic 37 (1998), no. 1, 35–47. MR 1672909, DOI 10.1007/BF02684083
- S. V. Vostokov, I. B. Zhukov, and G. K. Pak, Extensions with almost maximal depth of ramification, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 265 (1999), no. Vopr. Teor. Predst. Algebr i Grupp. 6, 77–109, 324–325 (2000) (Russian, with English and Russian summaries); English transl., J. Math. Sci. (New York) 112 (2002), no. 3, 4285–4302. MR 1757817, DOI 10.1023/A:1020382616985
- Takeshi Saito, Wild ramification and the characteristic cycle of an $l$-adic sheaf, J. Inst. Math. Jussieu 8 (2009), no. 4, 769–829. MR 2540880, DOI 10.1017/S1474748008000364
- Takeshi Saito, Wild ramification of schemes and sheaves, Proceedings of the International Congress of Mathematicians. Volume II, Hindustan Book Agency, New Delhi, 2010, pp. 335–356. MR 2827799
- Takeshi Saito, Ramification of local fields with imperfect residue fields III, Math. Ann. 352 (2012), no. 3, 567–580. MR 2885588, DOI 10.1007/s00208-011-0652-5
- Anthony J. Scholl, Higher fields of norms and $(\phi ,\Gamma )$-modules, Doc. Math. Extra Vol. (2006), 685–709. MR 2290602
- Jean-Pierre Serre, Corps locaux, Publications de l’Université de Nancago, No. VIII, Hermann, Paris, 1968 (French). Deuxième édition. MR 0354618
- Jean-Pierre Serre, Linear representations of finite groups, Graduate Texts in Mathematics, Vol. 42, Springer-Verlag, New York-Heidelberg, 1977. Translated from the second French edition by Leonard L. Scott. MR 0450380
- Victor P. Snaith, Explicit Brauer induction, Cambridge Studies in Advanced Mathematics, vol. 40, Cambridge University Press, Cambridge, 1994. With applications to algebra and number theory. MR 1310780, DOI 10.1017/CBO9780511600746
- Luca Spriano, Well ramified extensions of complete discrete valuation fields with applications to the Kato conductor, Canad. J. Math. 52 (2000), no. 6, 1269–1309. MR 1794305, DOI 10.4153/CJM-2000-053-1
- Luca Spriano, Well ramified extensions of complete discrete valuation fields with applications to the Kato conductor, Canad. J. Math. 52 (2000), no. 6, 1269–1309. MR 1794305, DOI 10.4153/CJM-2000-053-1
- Lara Thomas, Ramification groups in Artin-Schreier-Witt extensions, J. Théor. Nombres Bordeaux 17 (2005), no. 2, 689–720 (English, with English and French summaries). MR 2211314
- Yichao Tian, Canonical subgroups of Barsotti-Tate groups, Ann. of Math. (2) 172 (2010), no. 2, 955–988. MR 2680485, DOI 10.4007/annals.2010.172.955
- S. V. Vostokov and I. B. Zhukov, Some approaches to the construction of abelian extensions for ${\mathfrak {p}}$-adic fields, Proceedings of the St. Petersburg Mathematical Society, Vol. III, Amer. Math. Soc. Transl. Ser. 2, vol. 166, Amer. Math. Soc., Providence, RI, 1995, pp. 157–174. MR 1363296, DOI 10.1090/trans2/166/07
- Stefan Wewers, Fiercely ramified cyclic extensions of $p$-adic fields with imperfect residue field, Manuscripta Math. 143 (2014), no. 3-4, 445–472. MR 3167623, DOI 10.1007/s00229-013-0630-1
- Wayne Allen Whitney, Functorial Cohen rings, ProQuest LLC, Ann Arbor, MI, 2002. Thesis (Ph.D.)–University of California, Berkeley. MR 2707613
- Liang Xiao, On ramification filtrations and $p$-adic differential modules, I: the equal characteristic case, Algebra Number Theory 4 (2010), no. 8, 969–1027. MR 2832631, DOI 10.2140/ant.2010.4.969
- Liang Xiao, On ramification filtrations and $p$-adic differential equations, II: mixed characteristic case, Compos. Math. 148 (2012), no. 2, 415–463. MR 2904193, DOI 10.1112/S0010437X1100707X
- Liang Xiao, On the refined ramification filtrations in the equal characteristic case, Algebra Number Theory 6 (2012), no. 8, 1579–1667. MR 3033523, DOI 10.2140/ant.2012.6.1579
- —, Cleanness and log-characteristic cycles, I: vector bundles with flat connections, Math. Ann. (to appear); arXiv:1104.1224.
- I. B. Zhukov, Structure theorems for complete fields, Proceedings of the St. Petersburg Mathematical Society, Vol. III, Amer. Math. Soc. Transl. Ser. 2, vol. 166, Amer. Math. Soc., Providence, RI, 1995, pp. 175–192. MR 1363297, DOI 10.1090/trans2/166/08
- I. Zhukov, Milnor and topological $K$-groups of higher-dimensional complete fields, Algebra i Analiz 9 (1997), no. 1, 98–147 (Russian); English transl., St. Petersburg Math. J. 9 (1998), no. 1, 69–105. MR 1458420
- Igor Zhukov, Ramification of surfaces: Artin-Schreier extensions, Algebraic number theory and algebraic geometry, Contemp. Math., vol. 300, Amer. Math. Soc., Providence, RI, 2002, pp. 211–220. MR 1936374, DOI 10.1090/conm/300/05150
- —, Ramification of surfaces: sufficient jet order for wild jumps, Preprint, 2002, arXiv:math/0201071.
- I. B. Zhukov, On ramification theory in the case of an imperfect residue field, Mat. Sb. 194 (2003), no. 12, 3–30 (Russian, with Russian summary); English transl., Sb. Math. 194 (2003), no. 11-12, 1747–1774. MR 2052694, DOI 10.1070/SM2003v194n12ABEH000785
- I. B. Zhukov, Singularities of arcs and cyclic coverings of surfaces, Proceedings of the St. Petersburg Mathematical Society. Vol. XI, Amer. Math. Soc. Transl. Ser. 2, vol. 218, Amer. Math. Soc., Providence, RI, 2006, pp. 49–66. MR 2279304, DOI 10.1090/trans2/218/03
- I. B. Zhukov, Semiglobal models of extensions of two-dimensional local fields, Vestnik St. Petersburg Univ. Math. 43 (2010), no. 1, 33–38. MR 2662407, DOI 10.3103/S1063454110010061
- I. B. Zhukov, Ramification in elementary abelian extensions, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 413 (2013), no. Voprosy Teorii Predstavleniĭ Algebr i Grupp. 24, 106–114, 229 (Russian, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 202 (2014), no. 3, 404–409. MR 3073060, DOI 10.1007/s10958-014-2050-5
- —, Elementary Abelian conductor, Zap. Nauch. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 423 (2014), 126–131. (Russian)
Bibliographic Information
- L. Xiao
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, 196 Auditorium Road Unit 3009, Storrs, Connecticut 06269-3009
- MR Author ID: 888789
- Email: lxiao@math.uconn.edu
- I. Zhukov
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ pr. 28, Staryĭ Peterhof, 198504 St. Petersburg, Russia
- Email: i.zhukov@spbu.ru
- Received by editor(s): April 25, 2014
- Published electronically: July 27, 2015
- Additional Notes: The first author acknowledges support from Simons Foundation #278433 and CORCL research grant from University of California, Irvine. The second author acknowledges support from RFBR (projects nos. 11-01-00588-a and 14-01-00393-a)
- © Copyright 2015 American Mathematical Society
- Journal: St. Petersburg Math. J. 26 (2015), 695-740
- MSC (2010): Primary 11S15
- DOI: https://doi.org/10.1090/spmj/1355
- MathSciNet review: 3408704