# The Grothendieck ring of stacks

### Federico Scavia (UBC)

30-Jul-2021, 19:00-20:00 (20 months ago)

Abstract: The Grothendieck ring of algebraic stacks was introduced by T. Ekedahl in 2009, following up on work of other authors. It is a generalization of the Grothendieck ring of varieties. For every linear algebraic group $G$, we may consider the class of its classifying stack $BG$ in this ring. Computing the class of $BG$ is related to the famous rationality problem for fields of $G$-invariants (Noether's problem). I will give a brief introduction to the Grothendieck ring of stacks, and then talk about some of my results in this area.

algebraic geometry

Audience: researchers in the topic

( slides | video )

Comments: The synchronous discussion for Federico Scavia’s talk is taking place not in zoom-chat, but at tinyurl.com/2021-07-30-fs (and will be deleted after ~3-7 days).

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 Organizer: Ravi Vakil* *contact for this listing

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