On the vanishing of local cohomology in characteristic p > 0

Gennady Lyubeznik

doi:10.1112/S0010437X05001533

On the vanishing of local cohomology in characteristic p > 0

Gennady Lyubeznik

School of Mathematics

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

Abstract

Let R be a d-dimensional regular local ring of characteristic p > 0 with maximal ideal m, let I be an ideal of R and let A = R/I. We describe some properties of the local cohomology module H_Iⁱ(R), in particular its vanishing, in terms of the Frobenius action on the local cohomology module H_m^d-i(A).

Original language	English (US)
Pages (from-to)	207-221
Number of pages	15
Journal	Compositio Mathematica
Volume	142
Issue number	1
DOIs	https://doi.org/10.1112/S0010437X05001533
State	Published - 2006

Keywords

Characteristic p
Cohomological dimension
Frobenius
Local cohomology
Projective varieties

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10.1112/S0010437X05001533

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abstract = "Let R be a d-dimensional regular local ring of characteristic p > 0 with maximal ideal m, let I be an ideal of R and let A = R/I. We describe some properties of the local cohomology module HIi(R), in particular its vanishing, in terms of the Frobenius action on the local cohomology module Hmd-i(A).",

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author = "Gennady Lyubeznik",

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AB - Let R be a d-dimensional regular local ring of characteristic p > 0 with maximal ideal m, let I be an ideal of R and let A = R/I. We describe some properties of the local cohomology module HIi(R), in particular its vanishing, in terms of the Frobenius action on the local cohomology module Hmd-i(A).

KW - Characteristic p

KW - Cohomological dimension

KW - Frobenius

KW - Local cohomology

KW - Projective varieties

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JO - Compositio Mathematica

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On the vanishing of local cohomology in characteristic p > 0

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Keywords

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