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Tate's acyclicity theorem
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Analytic geometry
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Statement
Let $X = Spec_{an}(A)$ be an affinoid space with affinoid algebra $A$ .

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

(Berkovich 09, fact 2.2.6 )

References
S. Bosch, U. Güntzer, Reinhold Remmert , section 8.2 of Non-Archimedean Analysis – A systematic approach to rigid analytic geometry , 1984 (pdf )

Vladimir Berkovich , Non-archimedean analytic spaces , lectures at the Advanced School on $p$ -adic Analysis and Applications , ICTP, Trieste, 31 August - 11 September 2009 (pdf )

pdf

Doosung Park , Affinoid domains , lecture notes (pdf )

Last revised on July 18, 2014 at 00:46:35.
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