Title:  Smoothness of the cohomology sheaves of stacks of shtukas

Abstract:  Let X be a smooth projective geometrically connected curve over a finite field 𝔽_q. Let G be a connected reductive group over the function field of X. For every finite set I and every representation of (Ǧ)^I, where Ǧ is the Langlands dual group of G, we have a stack of shtukas over X^I. For every degree, we have a compact support ℓ-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.

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