Publications (24)
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…
Affine Beilinson-Bernstein localization at the critical level
David Yang, Sam Raskin
We prove the Frenkel-Gaitsgory localization conjecture describing regular Kac-Moody representations at critical level via eigensheaves on the affine Grassmannian using categorical…
On the notion of spectral decomposition in local geometric Langlands
Sam Raskin
The geometric Langlands program is distinguished in assigning spectral decompositions to all representations, not only the irreducible ones. However, it is not even clear what is m…
W-algebras and Whittaker categories
Sam Raskin
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space…
Coulomb branches of noncotangent type (with appendices by Gurbir Dhillon and Theo Johnson-Freyd)
Alexander Braverman, Gurbir Dhillon, Michael Finkelberg +2
We propose a construction of the Coulomb branch of a gauge theory corresponding to a choice of a connected reductive group and a symplectic finite-dimensio…
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…
Coherent sheaves on formal complete intersections via DG Lie algebras
Sam Raskin
We establish a criterion for sheaves on an adically complete DG scheme to be coherent. We deduce a description of coherent sheaves on an adically complete lci singularity in terms…
Homological methods in semi-infinite contexts
Sam Raskin
Actions of algebraic groups on DG categories provide a convenient, unifying framework in some parts of geometric representation theory, especially the representation theory of redu…
Affine Beilinson-Bernstein localization at the critical level for
Sam Raskin
We prove the rank 1 case of a conjecture of Frenkel-Gaitsgory: critical level Kac-Moody representations with regular central characters localize onto the affine Grassmannian. The m…
A generalization of the b-function lemma
Sam Raskin
We establish some cohomological bounds in D-module theory that are known in the holonomic case and folklore in general. The method rests on a generalization of the b-function lemma…
A Geometric Proof of the Feigin-Frenkel Theorem
Sam Raskin
We reprove the theorem of Feigin and Frenkel relating the center of the critical level enveloping algebra of the Kac-Moody algebra for a semisimple Lie algebra to opers (which are…
Non-vanishing of geometric Whittaker coefficients for reductive groups
Joakim Faergeman, Sam Raskin
We prove that cuspidal automorphic D-modules have non-vanishing Whittaker coefficients, generalizing known results in the geometric Langlands program from GL_n to general reductive…
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 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…
Acyclic complexes and 1-affineness
Dennis Gaitsgory, Sam Raskin
This short note is an erratum to arXiv:1306.4304, correcting the proof of one of its main results. It includes some counterexamples regarding infinite-dimensional unipotent groups…
Projective generation for equivariant -modules
Gwyn Bellamy, Sam Gunningham, Sam Raskin
We investigate compact projective generators in the category of equivariant -modules on a smooth affine variety. For a reductive group acting on a smooth affine variety ,…
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…
The Arinkin-Gaitsgory temperedness conjecture
Joakim Faergeman, Sam Raskin
Arinkin and Gaitsgory defined a category of tempered D-modules on Bun_G that is conjecturally equivalent to the category of quasi-coherent (not ind-coherent!) sheaves on LocSys_{\c…
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…
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…
On the Dundas-Goodwillie-McCarthy theorem
Sam Raskin
We give a modern presentation of the Dundas-Goodwillie-McCarthy theorem identifying relative K-theory and topological cyclic homology for nilpotent ring extensions.
Tate's thesis in the de Rham Setting
Justin Hilburn, Sam Raskin
We calculate the category of D-modules on the loop space of the affine line in coherent terms. Specifically, we find that this category is derived equivalent to the category of ind…
Exceptional loci in Lefschetz theory
Sam Raskin, Geoffrey Smith
Let be a morphism of varieties. Given a hyperplane in , there is a Gysin map from the compactly supported cohomology of $Ï^{-1}(H)…
Localization for affine -algebras
Gurbir Dhillon, Sam Raskin
We prove a localization theorem for affine -algebras in the spirit of Beilinson--Bernstein and Kashiwara--Tanisaki. More precisely, for any non-critical regular weight , we…