Now showing items 1-20 of 20

• #### Chiral Koszul Duality ﻿

(Springer, 2012)
We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004), ...
• #### Chiral Principal Series Categories ﻿

(2014-06-06)
This thesis begins a study of principal series categories in geometric representation theory using the Beilinson-Drinfeld theory of chiral algebras. We study Whittaker objects in the unramified principal series category. ...
• #### Compact Generation of the Category of D-Modules on the Stack of G-Bundles on a Curve ﻿

(2013)
The goal of the paper is to show that the (derived) category of D-modules on the stack $Bun_G(X)$ is compactly generated. Here X is a smooth complete curve, and G is a reductive group. The problem is that $Bun_G(X)$ ...
• #### Contractibility of the space of rational maps ﻿

(Springer Science + Business Media, 2012)
We define an algebro-geometric model for the space of rational maps from a smooth curve X to an algebraic group G, and show that this space is homologically contractible. As a consequence, we deduce that the moduli space ...
• #### A Corollary of the B-function Lemma ﻿

(Birkhäuser Basel, 2011)
• #### Deformations of Local Systems and Eisenstein Series ﻿

(Springer Science + Business Media, 2008)
• #### DG Indschemes ﻿

(American Mathematical Society, 2014)
We develop the notion of indscheme in the context of derived algebraic geometry, and study the categories of quasi-coherent sheaves and ind-coherent sheaves on indschemes. The main results concern the relation between ...
• #### Hecke Operators on Quasimaps into Horospherical Varieties ﻿

(University Bielefeld, Fakultat Mathematik, 2009)
Let G be a connected reductive complex algebraic group. This paper and its companion [GN06] are devoted to the space Z of meromorphic quasimaps from a curve into an affine spherical G-variety X. The space Z may be thought ...
• #### Ind-Coherent Sheaves ﻿

(Independent University of Moscow, 2013)
We develop the theory of ind-coherent sheaves on schemes and stacks. The category of ind-coherent sheaves is closely related, but inequivalent, to the category of quasi-coherent sheaves, and the difference becomes crucial ...
• #### Local Geometric Langlands Correspondence: The Spherical Case ﻿

(Mathematical Society of Japan, 2009)
A module over an affine Kac–Moody algebra $\hat{g}$ is called spherical if the action of the Lie subalgebra g[[t]] on it integrates to an algebraic action of the corresponding group G[[t]]. Consider the category of spherical ...
• #### Localization of $\hat{\mathfrak{g}}$-modules on the Affine Grassmannian ﻿

(Princeton University, 2009)
We consider the category of modules over the affine Kac-Moody algebra $\hat{\mathfrak{g}}$ of critical level with regular central character. In our previous paper we conjectured that this category is equivalent to the ...
• #### On Some Finiteness Questions for Algebraic Stacks ﻿

(Springer Science + Business Media, 2013)
We prove that under a certain mild hypothesis, the DG category of D-modules on a quasi-compact algebraic stack is compactly generated. We also show that under the same hypothesis, the functor of global sections on the DG ...
• #### Outline of the proof of the geometric Langlands conjecture for GL(2) ﻿

(Centre National de la Recherche Scientifique, 2015)
We outline a proof of the categorical geometric Langlands conjecture for GL_2, as formulated in Singular support of coherent sheaves and the geometric Langlands conjecture'', modulo a number of more tractable statements ...
• #### Picard-Lefschetz Oscillators for the Drinfeld-Lafforgue-Vinberg Compactification ﻿

(2015-05-01)
We study the singularities of the Drinfeld-Lafforgue-Vinberg compactification of the moduli stack of G-bundles on a smooth projective curve for a reductive group G. The study of these compactifications was initiated by V. ...
• #### Sheaves of categories and the notion of 1-affineness ﻿

(American Mathematical Society (AMS), 2015)
We define the notion of 1-affineness for a prestack, and prove an array of results that establish 1-affineness of certain types of prestacks.
• #### Singular support of coherent sheaves and the geometric Langlands conjecture ﻿

(Springer Science + Business Media, 2014)
We define the notion of singular support of a coherent sheaf on a quasi-smooth-derived scheme or Artin stack, where “quasi-smooth” means that it is a locally complete intersection in the derived sense. This develops the ...
• #### Twisted Whittaker Model and Factorizable Sheaves ﻿

(Birkhaeuser Verlag AG, 2008)
Let $G$ be a reductive group. The geometric Satake equivalence realized the category of representations of the Langlands dual group $\check G$ in terms of spherical perverse sheaves (or D-modules) on the affine ...
• #### Weyl Modules and Opers without Monodromy ﻿

(Springer-Verlag, 2010)
We prove that the algebra of endomorphisms of a Weyl module of critical level is isomorphic to the algebra of functions on the space of monodromy-free opers on the disc with regular singularity and residue determined by ...