Cohomological invariants and Brauer groups of algebraic stacks in positive characteristic

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.

47 pages, comments welcome! v2: we give a more general definition of cohomological invariants. We also made some small corrections throughout the paper. v3: accepted version. We fixeed some notation and added a remark at the end copmputing the pullback when changing base between finite fields of characteristic 2