Arbeitsgemeinschaft: The Geometric Langlands Conjecture

Abstract

The Langlands program is a vast, loosely connected, collection of theorems and conjectures. At quite different ends, there is the geometric Langlands program, which deals with perverse sheaves on the stack of G -bundles on a smooth projective curve, and the local Langlands program over p -adic fields, which deals with the representation theory of p -adic groups. Recently, inspired by applications to p-adic Hodge theory, Fargues and Fontaine hav..