Bun_G minicourse: Introduction

Abstract: This talk is the first part of a six-part series "$\mathrm{Bun}_G$, Shtukas, and the Local Langlands Program", held Tuesdays and Thursdays between 5 and 21 October, 2021.

Recordings and slides will appear here: sites.google.com/view/rampageseminar/home

Series abstract: The recent manuscript of Fargues-Scholze aims to "geometrize" the Langlands program for a p-adic group $G$, by relating the players in that story to the stack $\mathrm{Bun}_G$. Following a strategy of V. Lafforgue, the main result of [FS] is the construction of an L-parameter attached to a smooth irreducible representation of $G$.

The goal of this series is to review the main ideas of this work, and to discuss two related results: progress on the Kottwitz conjecture for local shtuka spaces by Hansen-Kaletha-Weinstein, and the construction of eigensheaves on $\mathrm{Bun}_G$ when $G=\mathrm{GL}_n$ by Anschütz-le Bras.

Talk abstract: We will give a historically motivated introduction to the story, reviewing moduli spaces of $p$-divisible groups, the Fargues-Fontaine curve, and the stack $\mathrm{Bun}_G$ of $G$-bundles on it. We will then define the moduli spaces of local shtukas, and state our result on their cohomology.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

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Recent Advances in Modern p-Adic Geometry (RAMpAGe)

Series comments: The Zoom Meeting ID is: 995 3670 1681. The password for the series is: *The first three-digit prime*. Please visit the external homepage for notes and videos from past talks.

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