Finiteness of cohomology of local systems on rigid analytic spaces

2016/11/21 by Kiran S. Kedlaya, Kedlaya, Kiran S., Ruochuan Liu +1
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1611.06930

openalex publication_date 2016/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the cohomology groups of an etale Q_p-local system on a smooth proper rigid analytic space are finite-dimensional Q_p-vector spaces, provided that the base field is either a finite extension of Q_p or an algebraically closed nonarchimedean field containing Q_p. This result manifests as a special case of a more general finiteness result for the higher direct images of a relative (phi, Gamma)-module along a smooth proper morphism of rigid analytic spaces over a mixed-characterstic nonarchimedean field.

Citations

• Relative p-adic Hodge theory, II: Imperfect period rings
• Notes on the A_inf-cohomology of Integral p-adic Hodge theory

Related

• Rigid non-cohomologically rigid local systems
• Étale cohomology of algebraizable rigid analytic varieties via nearby cycles over general bases
• De Rham comparison and Poincaré duality for rigid varieties
• G-rigid local systems are integral
• Crystalline cohomology of rigid analytic spaces