Abstract
Let f: X → S be a morphism between quasi-compact quasi-separated pseudo-adic spaces such that S is the spectrum of a separably algebraically closed analytic affinoid field, f is locally of algebraically finite type ((1.2.5)) (for example, f is smooth (1.7.7)) and X is a locally closed locally constructible subset of f−1(|S|). Let A be a noetherian ring which is annihilated by a natural number which is prime to char+(S), and let F be a constructible A-module on Xét. Then, for every n ∈ N0, the A-module Hn(X, F) is finitely generated.
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© 1996 Springer Fachmedien Wiesbaden
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Huber, R. (1996). Finiteness. In: Étale Cohomology of Rigid Analytic Varieties and Adic Spaces. Aspects of Mathematics, vol 30. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-09991-8_7
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DOI: https://doi.org/10.1007/978-3-663-09991-8_7
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-663-09992-5
Online ISBN: 978-3-663-09991-8
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