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 ...

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), ...

Let \(X\) be an algebraic variety, \(f\) a regular function, \(j:U \hookrightarrow X\) the complement to the locus of vanishing of \(f\), and \(M\) a holonomic D-module on \(U\). Consider the \(D_U[s]\)-module \(M\otimes ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...