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Science China Mathematics

, Volume 58, Issue 3, pp 565–632 | Cite as

Six operations and Lefschetz-Verdier formula for Deligne-Mumford stacks

  • Weizhe Zheng
Articles

Abstract

Laszlo and Olsson constructed Grothendieck’s six operations for constructible complexes on Artin stacks in étale cohomology under an assumption of finite cohomological dimension, with base change established on the level of sheaves. We give a more direct construction of the six operations for complexes on Deligne-Mumford stacks without the finiteness assumption and establish base change theorems in derived categories. One key tool in our construction is the theory of gluing finitely many pseudofunctors developed by Zheng (2014). As an application, we prove a Lefschetz-Verdier formula for Deligne-Mumford stacks. We include both torsion and -adic coefficients.

Keywords

Deligne-Mumford stack étale cohomology six operations pseudofunctor Lefschetz-Verdier formula 

MSC(2010)

14F20 14A20 18D05 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Morningside Center of Mathematics, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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