Cohomological invariants of algebraic stacks

TL;DR

This paper develops a theory of étale cohomological invariants for smooth Artin stacks, computes these invariants for elliptic curve stacks, and explores implications for Brauer groups of algebraic spaces.

Contribution

It introduces foundational concepts for invariants in étale cohomology of stacks and applies them to specific cases like elliptic curves and Brauer groups.

Findings

Computed invariants for the stack of elliptic curves

Established links between invariants and Brauer groups

Provided foundational framework for future research

Abstract

The purpose of this paper is to lay the foundations of a theory of invariants in \'etale cohomology for smooth Artin stacks. We compute the invariants in the case of the stack of elliptic curves, and we use the theory we developed to get some results regarding Brauer groups of algebraic spaces.