On the vanishing of local cohomology in characteristic p > 0

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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).

Original languageEnglish (US)
Pages (from-to)207-221
Number of pages15
JournalCompositio Mathematica
Volume142
Issue number1
DOIs
StatePublished - Dec 13 2006

Keywords

  • Characteristic p
  • Cohomological dimension
  • Frobenius
  • Local cohomology
  • Projective varieties

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