Duke Mathematical Journal

Finiteness of de Rham cohomology in rigid analysis

Elmar Grosse-Klönne

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Abstract

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

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

Dates
First available in Project Euclid: 18 June 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1087575225

Digital Object Identifier
doi:10.1215/S0012-7094-02-11312-X

Mathematical Reviews number (MathSciNet)
MR1905392

Zentralblatt MATH identifier
01820902

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

Citation

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. http://projecteuclid.org/euclid.dmj/1087575225.


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