The shift functor and the comprehensive factorization for internal groupoids
The six operations for sheaves on Artin stacks II: Adic coefficients
The structure of the tensor product of with a finite functor between -vector spaces
The paper studies the structure of functors in the category of functors from finite dimensional -vector spaces to -vector spaces, where is a finite functor and is the injective functor . A detection theorem is proved for sub-functors of such functors, which is the basis of the proof that the functors are artinian of type one.
The Taylor spectrum and quotient Banach spaces
Théorie des catégories semi-abéliennes
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...
Topological categories containing any category of algebras
Topological linear compactness for Grothendieck categories. Theorem of Tychonoff. Applications to coalgebras.
We show the Tychonoff's theorem for a Grothendieck category with a set of small projective generators. Strictly quasi-finite objects for semiartinian Grothendieck categories are characterized. We apply these results to the study of the Morita duality of dual algebra of a coalgebra.
Torsion Theories in Non-Additive Categories.
Triangulated categories of periodic complexes and orbit categories
We investigate the triangulated hull of orbit categories of the perfect derived category and the bounded derived category of a ring concerning the power of the suspension functor. It turns out that the triangulated hull corresponds to the full subcategory of compact objects of certain triangulated categories of periodic complexes. This specializes to Stai and Zhao’s result on the finite dimensional algebra of finite global dimension. As the first application, if , are flat algebras over a commutative...
Triples et exactitudes
Truncated microsupport and holomorphic solutions of D-modules
Tubular mutations
Two notes on radicals of Abelian groups
Two results of -exangulated categories
M. Herschend, Y. Liu, H. Nakaoka introduced -exangulated categories, which are a simultaneous generalization of -exact categories and -angulated categories. This paper consists of two results on -exangulated categories: (1) we give an equivalent characterization of axiom (EA2); (2) we provide a new way to construct a closed subfunctor of an -exangulated category.
Über projektive Moduln und Endlichkeitshindernisse bei Transformationsgruppen.
Un critère d’extension des foncteurs définis sur les schémas lisses
-fractional categories
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...