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On the vanishing of local cohomology in characteristic p > 0

Published online by Cambridge University Press:  13 January 2006

Gennady Lyubeznik
Gennady Lyubeznik
Affiliation:
Department of Mathematics, 206 Church Street SE, University of Minnesota, Minneapolis, MN 55455, USAgennady@math.umn.edu
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Abstract

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Let R be a d-dimensional regular local ring of characteristic p > 0 with maximal ideal $\mathfrak m$, 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 $H^{d-i}_{\mathfrak m}(A)$.

Keywords

local cohomologycharacteristic pFrobeniuscohomological dimensionprojective varieties13D45 (primary)14B15 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 1 , January 2006 , pp. 207 - 221
Copyright
Foundation Compositio Mathematica 2006