Cohomological Invariants for Algebraic Stacks

Robert Pirisi (Scuola Normale Superiore)

Cohomological invariants are arithmetic analogues of characteristc classes in topology, in which singular cohomology is replaced with ├ętale cohomology, and topological spaces with spectra of fields. Given an affine algebraic group G, a cohomological invariant for G is a way to assign functorially to each G-torsor over a field k an element of the cohomology ring of k. These invariants form a ring, which has been computed by several authors for many groups G. In my talk I will show how to extend the classic theory of cohomolgical invariants to Deligne-Mumford stacks, and compute the rings of invariants for stacks of elliptic curves, of curves of genus 2, and, more generally, of hyperelliptic curves of arbitrary genus.

Tuesday, April 29th, at 4:00pm in HBH 227

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