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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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Dedualizing complexes of bicomodules and MGM duality over coalgebras
TL;DR: In this article, the authors present the definition of a dedualizing complex of bisemimodules over a pair of semialgebras, and construct the related equivalence between the conventional or absolute derived categories of the abelian categories of semimmodules and semicontramodules.
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Perverse Sheaves on the Nilpotent Cone and Lusztig's Generalized Springer Correspondence
Laura Rider,Amber Russell +1 more
TL;DR: In this article, the authors consider perverse sheaves on the nilpotent cone and prove orthogonality relations for the equivariant category of sheaves in a method similar to Lusztig's for character sheaves.
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Dedualizing complexes of bicomodules and MGM duality over coalgebras
TL;DR: In this paper, the authors present the definition of a dedualizing complex of bicomodules over a pair of cocoherent co-associative coalgebras and construct an equivalence between the conventional or absolute derived categories of the abelian categories of semimodules and semicontramodules.
Resolutions and Moduli for Equivariant Sheaves over Toric Varieties
TL;DR: In this paper, the authors extended the combinatorial framework of toric geometry to equivariant sheaves over toric varieties and developed a formalism for describing equivariants by certain configurations of vector spaces.
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K-theoretic Hall algebras, quantum groups and super quantum groups.
Michela Varagnolo,Eric Vasserot +1 more
TL;DR: In this paper, it was shown that the K-theoretic Hall algebra of a preprojective algebra of affine type is isomorphic to the positive half of a quantum toroidal quantum group.