Finiteness of rigid cohomology with coefficients

Details Finiteness of rigid cohomology with coefficients Finiteness of rigid cohomology with coefficients

2002-08-04

arxiv.org/abs/math/0208027v6

preprint; published version: Duke Math. J. 134 (2006), 15-97

Mathematics

Algebraic Geometry

70 pages; v6: corrections to 8.3, 8.4, 9.3

Scientific paper

We prove that for any field k of characteristic p>0, any separated scheme X of finite type over k, and any overconvergent F-isocrystal E over X, the rigid cohomology H^i(X, E) and rigid cohomology with compact supports H^i_c(X,E) are finite dimensional vector spaces. We also establish Poincare duality and the Kunneth formula with coefficients. The arguments use a pushforward construction in relative dimension 1, based on a relative version of Crew's conjecture on the quasi-unipotence of certain p-adic differential equations.

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