Finiteness of rigid cohomology with coefficients
نویسنده
چکیده
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 rig(X, E) and rigid cohomology with compact supports H i c,rig(X, E) are finite dimensional vector spaces over an appropriate p-adic field. We also establish Poincaré duality and the Künneth 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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