Generic base change, Artin’s comparison theorem, and the decomposition theorem for complex Artin stacks
Author:
Shenghao Sun
Journal:
J. Algebraic Geom. 26 (2017), 513-555
DOI:
https://doi.org/10.1090/jag/683
Published electronically:
October 31, 2016
MathSciNet review:
3647792
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Abstract |
References |
Additional Information
Abstract: We prove the generic base change theorem for stacks and give an exposition on the lisse-analytic topos of complex analytic stacks, proving some comparison theorems between various derived categories of complex analytic stacks. This enables us to deduce the decomposition theorem for perverse sheaves on complex Artin stacks with affine stabilizers from the case over finite fields.
References
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- Bertrand Toën, $K$-Théorie et Cohomologie des Champs Algébriques: Théorèmes de Riemann-Roch, $\mathcal D$-Modules et Théorèmes “GAGA”, available at arXiv:math/9908097.
References
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- 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 (86g:32015)
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- Gérard Laumon and Laurent Moret-Bailly, Champs algébriques, 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. 39, Springer-Verlag, Berlin, 2000 (French). MR 1771927 (2001f:14006)
- 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 (2009f:14003a), DOI https://doi.org/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 (2009f:14003b), DOI https://doi.org/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 (2009j:14004), DOI https://doi.org/10.1007/s00209-008-0348-z
- James Milne, Lectures on Etale Cohomology (v2.10), 2008, www.jmilne.org/math/.
- Behrang Noohi, Foundations of topological stacks I, arXiv:math/0503247.
- Martin Olsson, Fujiwara’s theorem for equivariant correspondences, J. Algebraic Geom. 24 (2015), no. 3, 401–497. MR 3344762, DOI https://doi.org/10.1090/S1056-3911-2014-00628-7
- Martin C. Olsson, Compactifying moduli spaces for abelian varieties, Lecture Notes in Mathematics, vol. 1958, Springer-Verlag, Berlin, 2008. MR 2446415 (2009h:14072)
- Martin Olsson, Sheaves on Artin stacks, J. Reine Angew. Math. 603 (2007), 55–112. MR 2312554 (2008b:14002), DOI https://doi.org/10.1515/CRELLE.2007.012
- N. Spaltenstein, Resolutions of unbounded complexes, Compositio Math. 65 (1988), no. 2, 121–154. MR 932640 (89m:18013)
- Shenghao Sun, $L$-series of Artin stacks over finite fields, Algebra Number Theory 6 (2012), no. 1, 47–122. MR 2950161, DOI https://doi.org/10.2140/ant.2012.6.47
- Shenghao Sun, Decomposition theorem for perverse sheaves on Artin stacks over finite fields, Duke Math. J. 161 (2012), no. 12, 2297–2310. MR 2972459, DOI https://doi.org/10.1215/00127094-1723657
- Bertrand Toën, $K$-Théorie et Cohomologie des Champs Algébriques: Théorèmes de Riemann-Roch, $\mathcal D$-Modules et Théorèmes “GAGA”, available at arXiv:math/9908097.
Additional Information
Shenghao Sun
Affiliation:
Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, People’s Republic of China
MR Author ID:
986191
Received by editor(s):
January 8, 2015
Received by editor(s) in revised form:
September 16, 2015
Published electronically:
October 31, 2016
Article copyright:
© Copyright 2016
University Press, Inc.
