nLab
Tate's acyclicity theorem

Context

Analytic geometry

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Statement

Let X=Spec an(A)X = Spec_{an}(A) be an affinoid space with affinoid algebra AA.

Then for every finite cover of XX by affinoid domains, the corresponding Cech cohomology with coefficients in the structure sheaf AA, or with coefficients in any finite Banach module over AA, is concentrated in degree 0.

(Berkovich 09, fact 2.2.6)

References