Tensor products of categories of equivariant perverse sheaves
Tensor-triangulated categories and dualities.
Tertiary decomposition in Grothendieck categories
The Abelian defect group conjecture.
The algebraic theory of finiteness obstruction.
The category of groupoid graded modules
We introduce the abelian category R-gr of groupoid graded modules and give an answer to the following general question: If U: R-gr → R-mod denotes the functor which associates to any graded left R-module M the underlying ungraded structure U(M), when does either of the following two implications hold: (I) M has property X ⇒ U(M) has property X; (II) U(M) has property X ⇒ M has property X? We treat the cases when X is one of the properties: direct summand, free, finitely generated, finitely presented,...
The category of long exact sequences and the homotopy exact sequence of modules.
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 five- and nine-lemmas in P-semi-abelian categories.
The Gersten conjecture for Witt groups in the equicharacteristic case.
The Hermitian Morita theorems.
The homotopy category of chain complexes is a homotopy category
The Ker-Coker-sequence and its generalization in some classes of additive categories.
The Moore-Penrose inverse of a partitioned morphism in an additive category
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...