Lodh, Rémi Shankar: Galois cohomology of Fontaine rings. - Bonn, 2007. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-10795
@phdthesis{handle:20.500.11811/3098,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-10795,
author = {{Rémi Shankar Lodh}},
title = {Galois cohomology of Fontaine rings},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2007,
note = {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).},
url = {http://hdl.handle.net/20.500.11811/3098}
}

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