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Finiteness of de Rham cohomology in rigid analysis. (English) Zbl 1057.14023

Summary: 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 [Invent. Math. 128, 329–377 (1997; Zbl 0908.14005)] also in the nonsmooth case. We need a careful study of de Rham cohomology in situations of semistable reduction.

MSC:

14F30 \(p\)-adic cohomology, crystalline cohomology
14G22 Rigid analytic geometry
14F40 de Rham cohomology and algebraic geometry

Citations:

Zbl 0908.14005
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References:

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