Arithmetic Geometry

Let $G$ be a reductive Lie group. The Langlands classification describes the set $\Pi_a(G)$ of irreducible admissible $G$-representations in terms of conjugacy classes in the Langlands dual group. Inside $\Pi_a(G)$ is the subset $\Pi_u(G)$ of...

Fundamental Local Equivalence of Gaitsgory and Lurie is an instance of quantum local geometric Langlands correspondence. It asserts an equivalence between the affine category $O$ and the category of twisted Whittaker $D$-modules on the affine flag...