Cohomological invariants and Brauer groups of algebraic stacks in positive characteristic

TL;DR

This paper develops a new theory of cohomological invariants with mod p^r coefficients for algebraic stacks in characteristic p, enabling the complete computation of the Brauer group and invariants of the stack of elliptic curves.

Contribution

It introduces a novel framework for cohomological invariants in positive characteristic, advancing the understanding of algebraic stacks and their Brauer groups.

Findings

Complete computation of the Brauer group of the stack of elliptic curves.

Development of cohomological invariants theory with mod p^r coefficients.

Application of new tools to algebraic stacks in characteristic p.

Abstract

We introduce a theory of cohomological invariants with mod $p^r$ coefficients for algebraic stacks in characteristic $p$. Using these new tools we complete the computation of the Brauer group and cohomological invariants of the stack of elliptic curves over any field.