Duke Mathematical Journal

Finiteness of de Rham cohomology in rigid analysis

Elmar Grosse-Klönne

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For a large class of smooth dagger spaces–rigid spaces with overconvergent structure sheaf–we prove finite dimensionality of de Rham cohomology. This is enough to obtain finiteness of P. Berthelot's rigid cohomology also in the nonsmooth case. We need a careful study of de Rham cohomology in situations of semistable reduction.

Article information

Duke Math. J., Volume 113, Number 1 (2002), 57-91.

First available in Project Euclid: 18 June 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F30: $p$-adic cohomology, crystalline cohomology
Secondary: 14F40: de Rham cohomology [See also 14C30, 32C35, 32L10] 14G22: Rigid analytic geometry


Grosse-Klönne, Elmar. Finiteness of de Rham cohomology in rigid analysis. Duke Math. J. 113 (2002), no. 1, 57--91. doi:10.1215/S0012-7094-02-11312-X. https://projecteuclid.org/euclid.dmj/1087575225

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