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Article Dans Une Revue Algebra & Number Theory Année : 2013

Powers of ideals and the cohomology of stalks and fibers of morphisms.

Marc Chardin

Résumé

We first provide here a very short proof of a refinement of a theorem of Kodiyalam and Cutkosky, Herzog and Trung on the regularity of powers of ideals. This result implies a conjecture of Hà and generalizes a result of Eisenbud and Harris concerning the case of ideals primary for the graded maximal ideal in a standard graded algebra over a field. It also implies a new result on the regularities of powers of ideal sheaves. We then compare the cohomology of the stalks and the cohomology of the fibers of a projective morphism to the effect of comparing the maximums over fibers and over stalks of the Castelnuovo-Mumford regularities of a family of projective schemes.
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Dates et versions

hal-00874213 , version 1 (17-10-2013)

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Marc Chardin. Powers of ideals and the cohomology of stalks and fibers of morphisms.. Algebra & Number Theory, 2013, 7 (1), pp.1-18. ⟨10.2140/ant.2013.7-1⟩. ⟨hal-00874213⟩
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