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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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Canonical bases and KLR-algebras
Michela Varagnolo,E. Vasserot +1 more
TL;DR: In this article, the authors prove a conjecture of Khovanov-Lauda concerning the categorization of one half of the quantum group associated with a symmetric Cartan datum.
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Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence
TL;DR: In this article, the derived categories of DG-modules, DG-comodules, and DG-contramodules are considered, and the equivalence between the latter two categories is established.
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Hyperbolic localization of intersection cohomology
TL;DR: For a normal variety X defined over an algebraically closed field with an action of the multiplicative group T = Gm, this article showed that the hyperbolic localization of the intersection cohomology sheaf is a direct sum of intersection cohomeology sheaves.
Journal ArticleDOI
Compact corigid objects in triangulated categories and co- t -structures
TL;DR: In this article, Miyachi et al. showed that a compact corigid object of a triangulated category induces a structure similar to a t-structure which they shall call a co-tstructure, and also showed that the coheart of this non-degenerate co-Tstructure is equivalent to Mod(End(End(\( \mathcal{S} \))op), and hence an abelian subcategory of the category.
Book
Two Kinds of Derived Categories, Koszul Duality, and Comodule-Contramodule Correspondence
TL;DR: In this article, the derived categories of DG-modules, DG-comodules, and DG-contramodules were considered and the equivalence between the latter two categories was established.