Erratum to : “The finite free extension of artinian -algebras with the strong Lefschetz property” [Rend. Sem. Mat. Univ. Padova 110 (2003), 119–146]
Espace des germes d'arcs réels et série de Poincaré d'un ensemble semi-algébrique
Nous définissons l’espace des germes d’arcs réels tracés sur un ensemble semi-algébrique de , analogue réel de la théorie développée par Denef et Loeser concernant l’espace des germes d’arcs tracés sur une variété algébrique complexe. Puis, reprenant leur méthodes, nous prouvons la rationalité de la série de Poincaré associée à un ensemble semi-algébrique.
Étale -theory. II. Connections with algebraic -theory
Exact sequences of pairs in commutative rings
Exemple d'ouvert non agréable d'un spectre d'anneaux
Existence of Gorenstein projective resolutions and Tate cohomology
Existence of proper Gorenstein projective resolutions and Tate cohomology is proved over rings with a dualizing complex. The proofs are based on Bousfield Localization which is originally a method from algebraic topology.
Explicit computations around the Lichtenbaum-Harshorne vanishing theorem.
Extensions algébriques et formes quadratiques
Extensions of toric varieties.
Failure of splitting from module-finite extension rings.
Families of reduced zero-dimensional schemes.
A great deal of recent activity has centered on the question of whether, for a given Hilbert function, there can fail to be a unique minimum set of graded Betti numbers, and this is closely related to the question of whether the associated Hilbert scheme is irreducible or not. We give a broad class of Hilbert functions for which we show that there is no minimum, and hence that the associated Hilbert sheme is reducible. Furthermore, we show that the Weak Lefschetz Property holds for the general element...
Finitely generated Ext algebras.
Finiteness aspects of Gorenstein homological dimensions
We present an alternative way of measuring the Gorenstein projective (resp., injective) dimension of modules via a new type of complete projective (resp., injective) resolutions. As an application, we easily recover well known theorems such as the Auslander-Bridger formula. Our approach allows us to relate the Gorenstein global dimension of a ring R to the cohomological invariants silp(R) and spli(R) introduced by Gedrich and Gruenberg by proving that leftG-gldim(R) = maxleftsilp(R), leftspli(R),...
Finiteness of local homology modules
Let be an ideal of Noetherian ring and a finitely generated -module. In this paper, we introduce the concept of weakly colaskerian modules and by using this concept, we give some vanishing and finiteness results for local homology modules. Let , we will prove that for any integer
Finiteness properties of local cohomology modules (an application of D-modules to Commutative Algebra).
Fittings's Invariants and a Theorem of Grauert.
Flache T1-Stabilität in der Stratifizierung Verseller Entfaltungen.
Flat exterior Tor algebras and cotangent complexes.
F-modules: applications to local cohomology and D-modules in characteristic p>0.
Formal deformation of curves with group scheme action
We study equivariant deformations of singular curves with an action of a finite flat group scheme, using a simplified version of Illusie's equivariant cotangent complex. We apply these methods in a special case which is relevant for the study of the stable reduction of three point covers.