ARithmetische Geometrie OberSeminar Shtuka and the global Langlands correspondence,

Abstract

In this ARGOS we want to study the paper [VL] by V. La orgue where he proves the global Langlands conjecture for an arbitrary reductive group G over a function eld over a nite eld, in the direction from automorphic representations to Galois representations. In particular, this reproves L. La orgue's results, [LL], in the case of G = GLn. V. La orgue's arguments are very geometric, and rely on the geometric Satake equivalence of Mirkovi ¢ and Vilonen, [MV]. We will start by going through T. Richarz's paper on the geometric Satake equivalence, [R], and the de nition of shtukas and the analogue of the local model diagram in that setup, [VL, Section 2]