Let be an ideal of a commutative Noetherian ring . It is shown that the -modules are -cofinite for all finitely generated -modules and all if and only if the -modules and are -cofinite for all finitely generated -modules , and all integers .
Using a recently introduced correspondence of Emerton-Kisin we give a description of Lyubeznik’s local cohomology invariants in terms of local étale cohomology with coefficients.
In this paper we study a notion of local volume for Cartier divisors on arbitrary blow-ups of normal complex algebraic varieties of dimension greater than one, with a distinguished point. We apply this to study an invariant for normal isolated singularities, generalizing a volume defined by J. Wahl for surfaces. We also compare this generalization to a different one arising in recent work of T. de Fernex, S. Boucksom, and C. Favre.
We study, in certain cases, the notions of finiteness and stability of the set of associated primes and vanishing of the homogeneous pieces of graded generalized local cohomology modules.
Soit un germe de fonction analytique , à singularité isolée en . Nous nous proposons d’étudier le développement asymptotique des intégrales de formes , de degré , sur les fibres de . Nous montrons que ces développements asymptotiques peuvent être décrits à partir de l’action de la monodromie sur le groupe de la fibre de Milnor complexe.