On donne des propriétés de la catégorie tannakienne des modules de Dieudonné filtrés sur un corps $p$-adique (ces modules de Dieudonné jouent en $p$-adique un rôle analogue aux structures de Hodge complexes). On prouve l’existence d’un foncteur fibre sur ${\mathbf{Q}}_p$ et la simple connexité du groupe associé. Ceci permet de montrer, sous la conjecture de Fontaine : “faiblement admissible entraîne admissible”, une conjecture de Rapoport et Zink décrivant le torseur entre cohomologie cristalline et étale, et de prouver...

Given the category $X$ of coherent sheaves over a weighted projective line $X=X(\lambda ,p)$ (of any representation type), the endomorphism ring $\Sigma =\left(𝒯\right)$ of an arbitrary tilting sheaf - which is by definition an almost concealed canonical algebra - is shown to satisfy a rank additivity property (Theorem 3.2). Moreover, this property extends to the representationinfinite quasi-tilted algebras of canonical type (Theorem 4.2). Finally, it is demonstrated that rank additivity does not generalize to the case of tilting complexes...

We use a K-theory recipe of Thomason to obtain classifications of triangulated subcategories via refining some standard thick subcategory theorems. We apply this recipe to the full subcategories of finite objects in the derived categories of rings and the stable homotopy category of spectra. This gives, in the derived categories, a complete classification of the triangulated subcategories of perfect complexes over some commutative rings. In the stable homotopy category of spectra we obtain only...

We discuss the roots of the Nakayama and Auslander-Reiten translations in the derived category of coherent sheaves over a weighted projective line. As an application we derive some new results on the structure of selfinjective algebras of canonical type.

We develop the representation theory of selfinjective algebras which admit Galois coverings by the repetitive algebras of algebras whose derived category of bounded complexes of finite-dimensional modules is equivalent to the derived category of coherent sheaves on a weighted projective line with virtual genus greater than one.

Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let $(Q^{sg},I^{sg})$ and $(Q^g,I^g)$ be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra $K{Q}^{sg}/⟨I^{sg}⟩$ is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of $K{Q}^g/⟨I^g⟩$. As a corollary, we find that $gldimK{Q}^{sg}/⟨I^{sg}⟩<\infty$ if and only if $gldimKQ/⟨I⟩<\infty$ if and only if $gldimK{Q}^g/⟨I^g⟩<\infty$.

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 $G$, the derived and the stable categories of representations of a subgroup $H$ can be constructed out of the corresponding category for $G$ 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...

Let $\Lambda =\left(\begin{array}{cc}A& M\\ 0& B\end{array}\right)$ be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective $\Lambda$-modules under the condition that $M$ is a cocompatible $(A,B)$-bimodule, we establish a recollement of the stable category $\overline{\mathrm{Ginj}\left(\Lambda \right)}$. We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over $\Lambda$.

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.

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.