8 papers · 1 filter
Proof of the geometric Langlands conjecture V: the multiplicity one theorem
Dennis Gaitsgory, Sam Raskin
This is the final paper in the series of five, in which we prove the geometric Langlands conjecture (GLC). We conclude the proof of GLC by showing that there exists a unique (up to…
Applications of (higher) categorical trace I: the definition of AGCat
Dennis Gaitsgory, Nick Rozenblyum, Yakov Varshavsky
In this paper we record the formalism of algebro-geometric DG categories (in short AGCat) following a suggestion of V. Drinfeld. This formalism will be applied to ``real-world" pro…
Proof of the geometric Langlands conjecture I: construction of the functor
Dennis Gaitsgory, Sam Raskin
We construct the geometric Langlands functor in one direction (from the automorphic to the spectral side) in characteristic zero settings (i.e., de Rham and Betti). We prove that v…
Local and global Langlands conjecture(s) over function fields
Dennis Gaitsgory
This is a write-up for the plenary ICM talk, 2026. The goal of this paper is to propose a set of conjectures whose aim is to answer the basic question of the Langlands program (ove…
Geometric Langlands in positive characteristic from characteristic zero
Dennis Gaitsgory, Sam Raskin
We establish part of the statement of the geometric Langlands conjecture for l-adic sheaves over a field of positive characteristic. Namely, we show that the category of automorphi…
Proof of the geometric Langlands conjecture IV: ambidexterity
D. Arinkin, D. Beraldo, L. Chen +5
This paper performs the following steps toward the proof of GLC in the de Rham setting: (i) We deduce GLC for G=GL_n; (ii) We prove that the Langlands functor L_G constructed in [G…