×

On the crystalline period map. (English) Zbl 1351.14011

From the text: This article is a direct continuation by the author [J. Am. Math. Soc. 25, No. 3, 715–738 (2012; Zbl 1247.14018)]. It contains a simple proof of comparison theorems in \(p\)-adic Hodge theory (the Fontaine-Jannsen conjecture). Different proofs were found earlier by Faltings, Niziol, and Tsuji, the case of open varieties treated by Yamashita. An alternative approach, based on an identification of the log crystalline cohomology for lci maps with the noncompleted (for the Hodge filtration) derived de Rham complex, was developed by B. Bhatt, [“\(p\)-adic derived de Rham cohomology”, arxiv:1204.6560].

MSC:

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

Citations:

Zbl 1247.14018
PDFBibTeX XMLCite
Full Text: DOI arXiv