2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99811We 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.70 pages; v6: corrections to 8.3, 8.4, 9.3Algebraic GeometryNumber Theory14F30; 14F40, 14G22text