Beilinson, Alexander On the crystalline period map. (English) Zbl 1351.14011 Camb. J. Math. 1, No. 1, 1-51 (2013). 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]. Cited in 2 ReviewsCited in 22 Documents MSC: 14F30 \(p\)-adic cohomology, crystalline cohomology 14F40 de Rham cohomology and algebraic geometry 14F20 Étale and other Grothendieck topologies and (co)homologies Keywords:\(p\)-adic periods; log crystalline cohomology; \(h\)-topology; alterations Citations:Zbl 1247.14018 PDFBibTeX XMLCite \textit{A. Beilinson}, Camb. J. Math. 1, No. 1, 1--51 (2013; Zbl 1351.14011) Full Text: DOI arXiv