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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 \(Bun_G(X)\) ...
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 ...
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 ...
D-Modules on the Affine Flag Variety and Representations of Affine Kac-Moody Algebras
(American Mathematical Society, 2009)
The present paper studies the connection between the category of modules over the affine Kac-Moody Lie algebra at the critical level, and the category of D-modules on the affine flag scheme \(G((t))/I\), where \(I\) is the ...
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), ...
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 ...