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Equivariant Sheaves and Functors
Joseph Bernstein,Valery A. Lunts +1 more
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In this paper, the DG-modules and equivariant cohomology of toric varieties have been studied, and the derived category D G (X) and functors have been defined.Abstract:
Derived category D G (X) and functors.- DG-modules and equivariant cohomology.- Equivariant cohomology of toric varieties.read more
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Wall-crossing functors and -modules
TL;DR: In this article, translation functors and wall-crossing functors on infinite dimensional representations of a complex semisimple Lie algebra using D-modules are studied and a geometric interpretation of tilting modules is given.
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Derived equivalences by quantization
TL;DR: In this article, it was shown that given a smooth symplectic (in the algebraic sense) resolution $X$ of an affine algebraic variety $Y$ and an etale neighborhood of a point, the derived category of coherent sheaves on X$ is equivalent to the dervied category of finitely generated left modules over a non-commutative algebra $R$ in a sense close to that of M. Van den Bergh.
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Geometric Langlands duality and representations of algebraic groups over commutative rings
Ivan Mirković,Kari Vilonen +1 more
TL;DR: In this paper, a geometric version of the Satake isomorphism is given for a connected complex reductive algebraic group, where the category of representations of its Langlands dual is naturally equivalent to a certain category of perverse sheaves on the complex affine Grassmannian.
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Cohomological Donaldson-Thomas theory of a quiver with potential and quantum enveloping algebras
Ben Davison,Sven Meinhardt +1 more
TL;DR: The cohomological aspects of Donaldson-Thomas theory for Jacobi algebras and the associated cohomologically Hall algebra, introduced by Kontsevich and Soibelman, were studied in this paper.
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A motivated introduction to character sheaves and the orbit method for unipotent groups in positive characteristic
TL;DR: In this article, the character theory of finite nilpotent groups is discussed and a character sheaf for a unipotent group is introduced, and a toy model for the representation-theoretic notion of an L-packet is provided.