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Finiteness of rigid cohomology with coefficients

Kiran S. Kedlaya
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Abstract

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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Kiran S. Kedlaya. 2005-11-03. Finiteness of rigid cohomology with coefficients. https://arxiv.org/abs/math/0208027

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