Local cohomology multiplicities in in terms of étale cohomolgy

Details Local cohomology multiplicities in in terms of étale cohomolgy Local cohomology multiplicities in in terms of étale cohomolgy

2004-06-14

arxiv.org/abs/math/0406265v2

Ann. Inst. Fourier, 55, 7 (2005), 2239-2256

Mathematics

Algebraic Geometry

15 pages, journal reference added, corrected statement of main result

Scientific paper

We give a description of certain local cohomology invariants (introduced by Lyubeznik) for a class of mildly singular varieties in positive characteristic. The novelty of our approuch lies in using the new Riemann-Hilbert type correspondenc of Emerton and Kisin to express these invariants in terms of 'etale cohomology with ZZ/pZZ coefficients. Thus we are able to obtain results in positive characteristic whereas earlier approaches were restricted (due to the use of de Rham theory) to the analytic case.

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