Motivic homotopy theory of algebraic stacks

by Chirantan Chowdhury (University of Duisburg-Essen)

Friday 11 Mar 2022, 11:30 → 13:30 Europe/Moscow

818-1526-4739 (Zoom)

In this talk, we extend the stable motivic homotopy theory from schemes to a large class of algebraic stacks using the language of $\infty$-categories. This includes quasi-separated algebraic spaces, local quotient stacks (for example moduli of vector bundles). We also extend the six functor formalism and prove statements like localization and purity.

We start the talk by motivating the need of such specific class of algebraic stacks which shall lead up to the construction of the stable homotopy functor and the four functors $f^*$, $f_*$, $-\otimes -$ and $\mathrm{Hom}(-,-)$. Then we briefly explain the construction of the exceptional functors, base change and projection formula using the so called ”Enhanced Operation Map” due to Liu and Zheng. The talk ends by stating the other properties of these six functors like localization and purity.

Video