Tensor products of categories of equivariant perverse sheaves
Tensor-triangulated categories and dualities.
The Abelian defect group conjecture.
The connection between May's axioms for a triangulated tensor product and Happel's description of the derived category of the quiver .
The connection between the -theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel
The differential Galois theory of regular singular p-adic differential equations.
The dimension of the derived category of elliptic curves and tubular weighted projective lines
We show that the dimension of the derived category of an elliptic curve or a tubular weighted projective line is one. We give explicit generators realizing this number, and show that they are in a certain sense minimal.
The Extraordinary Derived Category.
The Gersten conjecture for Witt groups in the equicharacteristic case.
The Mukai pairing. I: A categorical approach.
The representation dimension of domestic weakly symmetric algebras
Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras...
The six operations for sheaves on Artin stacks II: Adic coefficients
Thick subcategories of the stable module category
We study the thick subcategories of the stable category of finitely generated modules for the principal block of the group algebra of a finite group G over a field of characteristic p. In case G is a p-group we obtain a complete classification of the thick subcategories. The same classification works whenever the nucleus of the cohomology variety is zero. In case the nucleus is nonzero, we describe some examples which lead us to believe that there are always infinitely many thick subcategories concentrated...
Tilting Bundles on Rational Surfaces and Quasi-Hereditary Algebras
Let be any rational surface. We construct a tilting bundle on . Moreover, we can choose in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on is equivalent to the bounded derived category of finitely generated modules over a finite dimensional quasi-hereditary algebra . The construction starts with a full exceptional sequence of line bundles on and uses universal extensions. If is any smooth projective variety...
Truncated microsupport and holomorphic solutions of D-modules
Tubular mutations
Un critère d’extension des foncteurs définis sur les schémas lisses
Vector bundles on plane cubic curves and the classical Yang–Baxter equation
In this article, we develop a geometric method to construct solutions of the classical Yang–Baxter equation, attaching a family of classical -matrices to the Weierstrass family of plane cubic curves and a pair of coprime positive integers. It turns out that all elliptic -matrices arise in this way from smooth cubic curves. For the cuspidal cubic curve, we prove that the obtained solutions are rational and compute them explicitly. We also describe them in terms of Stolin’s classication and prove...
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