Galois cohomology of Fontaine rings
Galois cohomology of Fontaine rings
dc.contributor.advisor | Faltings, Gerd | |
dc.contributor.author | Lodh, Rémi Shankar | |
dc.date.accessioned | 2020-04-10T15:40:45Z | |
dc.date.available | 2020-04-10T15:40:45Z | |
dc.date.issued | 2007 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/3098 | |
dc.description.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). | |
dc.language.iso | eng | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | algebraic geometry | |
dc.subject | arithmetic geometry | |
dc.subject | etale cohomology | |
dc.subject | crystalline cohomology | |
dc.subject | p-adic Hodge theory | |
dc.subject.ddc | 510 Mathematik | |
dc.title | Galois cohomology of Fontaine rings | |
dc.type | Dissertation oder Habilitation | |
dc.publisher.name | Universitäts- und Landesbibliothek Bonn | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.identifier.urn | https://nbn-resolving.org/urn:nbn:de:hbz:5N-10795 | |
ulbbn.pubtype | Erstveröffentlichung | |
ulbbnediss.affiliation.name | Rheinische Friedrich-Wilhelms-Universität Bonn | |
ulbbnediss.affiliation.location | Bonn | |
ulbbnediss.thesis.level | Dissertation | |
ulbbnediss.dissID | 1079 | |
ulbbnediss.date.accepted | 05.06.2007 | |
ulbbnediss.fakultaet | Mathematisch-Naturwissenschaftliche Fakultät | |
dc.contributor.coReferee | Ramero, Lorenzo |
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