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

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. 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 $\ell$-adic coefficients.

62 pages. v5, v4: minor improvements; v3: added a Lefschetz-Verdier formula; v2: moved the appendix in v1 to arXiv:1211.1877

References in corpus (2)

• Odds and ends on finite group actions and traces
• Existence and properties of geometric quotients

Cited by in corpus (6)

• Duality and nearby cycles over general bases
• Parity and symmetry in intersection and ordinary cohomology
• Categorical traces and a relative Lefschetz-Verdier formula
• Gluing pseudo functors via $n$-fold categories
• Compatible systems and ramification
• Vanishing of Brauer groups of moduli stacks of stable curves