4 papers
Tempered vs generic automorphic functions and the canonical filtration on automorphic functions
Dennis Gaitsgory, Vincent Lafforgue, Sam Raskin
We introduce and study the filtration on the space of automorphic functions (in the everywhere unramified situation for the function field case) obtained by transferring the filtra…
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…
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…
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…