8 citations · 16 across the 9 of their papers we have counts for
9 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…
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…
Proof of the geometric Langlands conjecture III: compatibility with parabolic induction
Justin Campbell, Lin Chen, Joakim Faergeman +4
We establish the compatibility of the Langlands functor with the operations of Eisenstein series constant term, and deduce that the Langlands functor induces an equivalence on Eise…
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 II: Kac-Moody localization and the FLE
D. Arinkin, D. Beraldo, J. Campbell +6
This paper is the second in a series of five that together prove the geometric Langlands conjecture. Our goals are two-fold: (1) Formulate and prove the Fundamental Local Equivalen…
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…
Langlands duality on the Beilinson-Drinfeld Grassmannian
Justin Campbell, Sam Raskin
We calculate various categories of equivariant sheaves on the Beilinson-Drinfeld Grassmannian in Langlands dual terms. For one, we obtain the factorizable derived geometric Satake…
Fundamental local equivalences in quantum geometric Langlands
Justin Campbell, Gurbir Dhillon, Sam Raskin
In quantum geometric Langlands, the Satake equivalence plays a less prominent role than in the classical theory. Gaitsgory--Lurie proposed a conjectural substitute, later termed th…