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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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Duality and Tilting for Commutative DG Rings
TL;DR: In this paper, the existence and uniqueness of rigid DG modules over commutative DG rings were studied. But the results of these studies were restricted to the case of DG rings with non-positive strongly commutive associative unital DG algebras.
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The cohomological Hall algebra of a surface and factorization cohomology
Mikhail Kapranov,Eric Vasserot +1 more
TL;DR: For a smooth quasi-projective surface S over complex numbers, the Borel-Moore homology of the stack of coherent sheaves on S with compact support was studied in this paper.
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The Geometric Weil Representation
Shamgar Gurevich,Ronny Hadani +1 more
TL;DR: In this paper, a geometric analogue of the Weil representation over a finite field is constructed, which eliminates most of the unpleasant formulas that appear in the traditional (non-invariant) approaches and puts in the forefront some delicate geometric phenomena which underlie this representation.
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On Serre duality for compact homologically smooth DG algebras
TL;DR: In this article, a Serre functor on the category of perfect modules over an arbitrary compact and smooth DG algebra is presented, which is used to prove the existence of a non-degenerate pairing on the Hochschild homology of the DG algebra.
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Modular perverse sheaves on flag varieties II: Koszul duality and formality
Pramod N. Achar,Simon Riche +1 more
TL;DR: In this article, a formalism of mixed modular perverse sheaves for varieties equipped with a stratification by affine spaces was developed, based on the theory of parity sheaves due to Juteau-Mautner-Williamson.