$L$-series of Artin stacks over finite fields

Abstract

We develop the notion of stratifiability in the context of derived categories and the six operations for stacks. Then we reprove the Lefschetz trace formula for stacks, and give the meromorphic continuation of $L$-series (in particular, zeta functions) of ${\mathbb{F}}_q$-stacks. We also give an upper bound for the weights of the cohomology groups of stacks, and an “independence of $\ell$” result for a certain class of quotient stacks.