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Cohomological descent in rigid cohomology. (English) Zbl 1073.14026

Adolphson, Alan (ed.) et al., Geometric aspects of Dwork theory. Vol. I, II. Berlin: Walter de Gruyter (ISBN 3-11-017478-2/hbk). 931-981 (2004).
Summary: This is a survey of cohomological descent in rigid cohomology which was studied by B. Chiarellotto and the author. The notion of universally cohomological descendability and universally de Rham descendability for hypercoverings of triples plays an important role in the theory. We explain the notion, and give an idea of the proof of universally cohomological descendability and universally de Rham descendability of étale (resp. proper) hypercoverings. We show how to construct an embedding system for truncated simplicial schemes and prove the existence of spectral sequences for rigid cohomology with respect to given étale (resp. proper) hypercoverings. Finally we give applications to the finiteness theorem and the weight theory in rigid cohomology.
For the entire collection see [Zbl 1047.14001].

MSC:

14F30 \(p\)-adic cohomology, crystalline cohomology
14F40 de Rham cohomology and algebraic geometry
14F20 Étale and other Grothendieck topologies and (co)homologies
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