Algebraic Geometry Seminar

In a recent joint work with Kedlaya, we prove that the cohomology groups of an étale Qp-local system on a smooth proper rigid analytic space are finite-dimensional Qp-vector spaces, provided that the base field is either a finite extension of Qp or an algebraically closed nonarchimedean field containing Qp. This result manifests as a special case of a more general finiteness result for the higher direct images of a relative (ϕ,Γ)-module along a smooth proper morphism of rigid analytic spaces over a mixed-characterstic nonarchimedean field.