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On Faltings’ method of almost étale extensions. (English) Zbl 1175.14012

Abramovich, D. (ed.) et al., Algebraic geometry, Seattle 2005. Proceedings of the 2005 Summer Research Institute, Seattle, WA, USA, July 25–August 12, 2005. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4703-9/hbk; 978-0-8218-4057-3/set). Proceedings of Symposia in Pure Mathematics. 80, Pt. 2, 811-936 (2009).
The paper gives a detailed account of the reviewer’s proof of Fontaine’s conjecture relating \(p\)-adic étale and crystalline cohomology, for varieties with good reduction. The exposition uses almost étale coverings and follows the original path, with some modifications in details which are usually fortunate and occasionally not. (However, I could not find any serious flaws).
For the entire collection see [Zbl 1158.14004].

MSC:

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