2010/06/30 by Weizhe Zheng · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14A20 #msc:14F20 #msc:18D05
paper · pdf · doi:10.1007/s11425-015-4970-z
published as Sci. China Math. 58 (2015), no. 3 (special issue for the fifth Algebraic Geometry in East Asia conference), 565-632 · 62 pages. v5, v4: minor improvements; v3: added a Lefschetz-Verdier formula; v2: moved the appendix in v1 to arXiv:1211.1877
arxiv created 2014/12/27 · openalex publication_date 2015/01/22 · arxiv updated 2015/02/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
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. In this article 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 in arXiv:1211.1877. As an application, we prove a Lefschetz-Verdier formula for Deligne-Mumford stacks. We include both torsion and ℓ-adic coefficients.