16 citations · 36 across the 7 of their papers we have counts for
7 papers
Automorphic functions as the trace of Frobenius
D. Arinkin, D. Gaitsgory, D. Kazhdan +3
We prove that the trace of the Frobenius endofunctor of the category of automorphic sheaves with nilpotent singular support maps isomorphically to the space of unramified automorph…
Duality for automorphic sheaves with nilpotent singular support
D. Arinkin, D. Gaitsgory, D. Kazhdan +3
We identify the category Shv_{Nilp}(Bun_G) of automorphic sheaves with nilpotent singular support with its own dual, and relate this structure to the Serre functor on Shv_{Nilp}(Bu…
The stack of local systems with restricted variation and geometric Langlands theory with nilpotent singular support
D. Arinkin, D. Gaitsgory, D. Kazhdan +3
We define a new geometric object--the stack of local systems with restricted variation. We formulate a version of the categorical geometric Langlands conjecture that makes sense fo…
A toy model for the Drinfeld-Lafforgue shtuka construction
D. Gaitsgory, D. Kazhdan, N. Rozenblyum +1
The goal of this paper is to provide a categorical framework that leads to the definition of shtukas à la Drinfeld and of excursion operators à la V. Lafforgue. We take as the poin…
Singular support of coherent sheaves, and the geometric Langlands conjecture
Dima Arinkin, Dennis Gaitsgory
We develop the notion of singular support of a coherent sheaf on a quasi-smooth DG scheme or stack and use it to formulate the Geometric Langlands Conjecture.
A corollary of the b-function lemma
Alexander Beilinson, Dennis Gaitsgory
Let be an algebraic variety, a regular function, the complement to the locus of vanishing of , and a holonomic D-module on . Consider the -…
Geometric Realization of Whittaker Functions and the Langlands Conjecture
E. Frenkel, D. Gaitsgory, D. Kazhdan +1
We prove the equivalence of two conjectural constructions of unramified cuspidal automorphic functions on the adelic group GL_n(A) associated to an irreducible l-adic local system…