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  Galois cohomology of Fontaine rings

Lodh, R. S. (2007). Galois cohomology of Fontaine rings. PhD Thesis, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0004-2B9C-D Version Permalink: https://hdl.handle.net/21.11116/0000-0009-009E-5
Genre: Thesis

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Lodh_Galois cohomology_2007.pdf (Any fulltext), 665KB
 
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 Creators:
Lodh, Rémi Shankar1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 Abstract: Let $V$ be a complete discrete valuation ring of mixed characteristic. We express the crystalline cohomology of the special fibre of certain smooth affine $V$-schemes $X=Spec(R)$ tensored with an appropriate ring of $p$-adic periods as the Galois cohomology of the fundamental group of the geometric generic fibre $\pi_1(X_{\bar{V}[1/p]})$ with coefficients in a Fontaine ring constructed from $R$. This is based on Faltings' approach to $p$-adic Hodge theory (the theory of almost étale extensions). Using this we deduce maps from $p$-adic étale cohomology to crystalline cohomology of smooth $V$-schemes. The results are more general, as the semi-stable case is also considered. In the end we derive an alternative proof of the theorem of Tsuji (the semi-stable conjecture of Fontaine-Jannsen).

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Language(s): eng - English
 Dates: 2007
 Publication Status: Accepted / In Press
 Pages: 79 p.
 Publishing info: Bonn : Rheinische Friedrich-Wilhelms-Universität Bonn
 Table of Contents: -
 Rev. Type: -
 Identifiers: URN: https://nbn-resolving.org/urn:nbn:de:hbz:5N-10795
 Degree: PhD

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