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Finiteness of cohomology of local systems on rigid analytic spaces

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arxiv 1611.06930 v1 pith:QPRYVRYG submitted 2016-11-21 math.NT math.AG

Kiran S. Kedlaya , Ruochuan Liu This is my paper · ORCID
classification math.NTmath.AG
keywords analyticfieldrigidspacescohomologyfinitenessnonarchimedeanproper
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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.

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Cited by 1 Pith paper

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  1. A 6-functor formalism for solid quasi-coherent sheaves on the Fargues-Fontaine curve

    math.AG 2024-12 accept novelty 7.0 of 10

    A 6-functor formalism for Z_p-linear solid quasi-coherent sheaves on small v-stacks is constructed, yielding Poincare duality for pro-etale Q_p-cohomology.

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