  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.
