Smoothness of the cohomology sheaves of stacks of shtukas

Abstract: Let $X$ be a smooth projective geometrically connected curve over a finite field $\mathbb{F}_q$. Let $G$ be a connected reductive group over the function field of $X$. For every finite set $I$ and every representation of $(\check{G})^I$, where $\check{G}$ is the Langlands dual group of $G$, we have a stack of shtukas over $X^I$. For every degree, we have a compact support $\ell$-adic cohomology sheaf over $X^I$.

In this talk, I will recall some properties of these sheaves. I will talk about a work in progress which proves that these sheaves are ind-smooth over $X^I$.

algebraic geometrynumber theory

Audience: researchers in the topic

( slides )

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MIT number theory seminar

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