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Now showing items 1-10 of 11

#### Anabelian Intersection Theory

(2012-12-19)

Let F be a field finitely generated and of transcendence degree 2 over \(\bar{\mathbb{Q}}\). We describe a correspondence between the smooth algebraic surfaces X defined over \(\bar{\mathbb{Q}}\) with field of rational ...

#### 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), ...

#### Abundance Conjecture

(International Press, 2010)

We sketch a proof of the abundance conjecture that the Kodaira dimension of a compact complex algebraic manifold equals its numerical Kodaira dimension. The proof consists of the following three parts: (i) the case of ...

#### 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 ...

#### Shimura Curves for Level-3 Subgroups of the (2,3,7) Triangle Group and Some Other Examples

(Springer Verlag, 2006)

The (2,3,7) triangle group is known to be associated with a quaternion algebra A/K ramified at two of the three real places of K=Q(cos2π/7) and unramified at all other places of K. This triangle group and its congruence ...

#### 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 ...

#### Regeneration of Elliptic Chains with Exceptional Linear Series

(2014-06-06)

We study two dimension estimates regarding linear series on algebraic curves. First, we generalize the classical Brill-Noether theorem to many cases where the Brill-Noether number is negative. Second, we extend results of ...

#### 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 \(Bun_G(X)\) ...