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Cascades in the Dynamics of Measured Foliations
(Elsevier Masson, 2014-03-14)
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 ...
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 ...
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 ...
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 ...
Knots which Behave Like the Prime Numbers
(Oxford University Press (OUP), 2013)
This paper establishes a version of the Chebotarev density theorem in which number fields are replaced by 3-manifolds.
Moduli Spaces in Genus Zero and Inversion of Power Series
(Swets & Zeitlinger, 2014-03-11)
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 ...