Diffeotopy functors of ind-algebras and local cyclic cohomology.
Distinguishing derived equivalence classes using the second Hochschild cohomology group
We study the second Hochschild cohomology group of the preprojective algebra of type D₄ over an algebraically closed field K of characteristic 2. We also calculate the second Hochschild cohomology group of a non-standard algebra which arises as a socle deformation of this preprojective algebra and so show that the two algebras are not derived equivalent. This answers a question raised by Holm and Skowroński.
Divisible and Codivisible Modules.
Dualité relative en géométrie analytique complexe.
Dualization in algebraic K-theory and the invariant e¹ of quadratic forms over schemes
In the classical Witt theory over a field F, the study of quadratic forms begins with two simple invariants: the dimension of a form modulo 2, called the dimension index and denoted e⁰: W(F) → ℤ/2, and the discriminant e¹ with values in k₁(F) = F*/F*², which behaves well on the fundamental ideal I(F)= ker(e⁰). Here a more sophisticated situation is considered, of quadratic forms over a scheme and, more generally, over an exact category with duality. Our purposes are: ...
Endomorphism rings of maximal rigid objects in cluster tubes
We describe the endomorphism rings of maximal rigid objects in the cluster categories of tubes. Moreover, we show that they are gentle and have Gorenstein dimension 1. We analyse their representation theory and prove that they are of finite type. Finally, we study the relationship between the module category and the cluster tube via the Hom-functor.
Enlargements of categories.
Enriched model categories and an application to additive endomorphism spectra.
Equivariant sheaves on toric varieties
Essential localizations and infinitary exact completion.
Essential properties of pro-objects in Grothendieck categories
Étude élémentaire des catégories
Exact completion and representations in abelian categories.
Exact couples in a Raïkov semi-abelian category
Exceptional collections on isotropic Grassmannians
We introduce a new construction of exceptional objects in the derived category of coherent sheaves on a compact homogeneous space of a semisimple algebraic group and show that it produces exceptional collections of the length equal to the rank of the Grothendieck group on homogeneous spaces of all classical groups.
Explicit cogenerators for the homotopy category of projective modules over a ring
Let be a ring. In two previous articles [12, 14] we studied the homotopy category of projective -modules. We produced a set of generators for this category, proved that the category is -compactly generated for any ring , and showed that it need not always be compactly generated, but is for sufficiently nice . We furthermore analyzed the inclusion and the orthogonal subcategory . And we even showed that the inclusion has a right adjoint; this forces some natural map to be an equivalence...
Explicit models for perserse sheaves.
We consider categories of generalized perverse sheaves, with relaxed constructibility conditions, by means of the process of gluing t-structures and we exhibit explicit abelian categories defined in terms of standard sheaves categories which are equivalent to the former ones. In particular , we are able to realize perverse sheaves categories as non full abelian subcategories of the usual bounded complexes of sheaves categories. Our methods use induction on perversities. In this paper, we restrict...
Ext and von Neumann regular rings
Ext-algebras and derived equivalences
Using derived categories, we develop an alternative approach to defining Koszulness for positively graded algebras where the degree zero part is not necessarily semisimple.
Extension categories and their homotopy