Some remarks on global dimensions for cotorsion pairs
Sous-catégories pleines d'une catégorie dérivée filtrée
Sous-quotients et relations induites dans les catégories exactes
Stable and costable preradicals
Stable derived functors of the second symmetric power functor, second exterior power functor and Whitehead gamma functor
Stable short exact sequences and the maximal exact structure of an additive category
It was recently proved that every additive category has a unique maximal exact structure, while it remained open whether the distinguished short exact sequences of this canonical exact structure coincide with the stable short exact sequences. The question is answered by a counterexample which shows that none of the steps to construct the maximal exact structure can be dropped.
Stable tubes in extriangulated categories
Let be a semibrick in an extriangulated category. If is a -semibrick, then the Auslander-Reiten quiver of the filtration subcategory generated by is . If is a -cycle semibrick, then is .
Stacks of group representations
We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group , the derived and the stable categories of representations of a subgroup can be constructed out of the corresponding category for by a purely triangulated-categorical construction, analogous to étale extension in algebraic geometry. In the case of finite groups, we then use descent methods to investigate...
Strict modules and homotopy modules in stable homotopy.
(Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras
Let be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective -modules under the condition that is a cocompatible -bimodule, we establish a recollement of the stable category . We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over .
Structure of additive categories
Subcategories of the derived category and cotilting complexes
We show that there is a one-to-one correspondence between basic cotilting complexes and certain contravariantly finite subcategories of the bounded derived category of an artin algebra. This is a triangulated version of a result by Auslander and Reiten. We use this to find an existence criterion for complements to exceptional complexes.
Subspaces in abstract Stone duality.
Suite spectrale du coniveau et -structure homotopique
Dans cette note, nous montrons que la suite spectrale du coniveau associée à un spectre motivique sur un corps parfait coïncide avec sa suite spectrale d’hypercohomologie pour la t-structure homotopique.
Sur la notion de localisation exacte et de localisation plate
Sur les algebres de Rees II.
Sur les catégories préadditives topologiques
Sur les quasi-limites
Sur l’homologie des groupes orthogonaux et symplectiques à coefficients tordus
On calcule dans cet article l’homologie stable des groupes orthogonaux et symplectiques sur un corps fini à coefficients tordus par un endofoncteur usuel des -espaces vectoriels (puissance extérieure, symétrique, divisée...). Par homologie stable, on entend, pour tout entier naturel , les colimites des espaces vectoriels et — dans cette situation, la stabilisation (avec une borne explicite en fonction de et ) est un résultat classique de Charney. Tout d’abord, nous donnons un cadre...
-forms and their properties.