Caruso, Xavier An introduction to \(p\)-adic period rings. (English) Zbl 1443.13018 Andreatta, Fabrizio et al., An excursion into \(p\)-adic Hodge theory: from foundations to recent trends. Paris: Société Mathématique de France (SMF). Panor. Synth. 54, 19-92 (2019). Summary: This paper is the augmented notes of a course I gave jointly with Laurent Berger in Rennes in 2014. Its aim was to introduce the periods rings \(B_{\mathrm{crys}}\) and \(B_{\mathrm{dR}}\) and state several comparison theorems between étale and crystalline or de Rham cohomologies for \(p\)-adic varieties.For the entire collection see [Zbl 1430.14001]. MSC: 13F35 Witt vectors and related rings 11F80 Galois representations 11S20 Galois theory 11S15 Ramification and extension theory 14F30 \(p\)-adic cohomology, crystalline cohomology 14G20 Local ground fields in algebraic geometry 14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry Keywords:\(p\)-adic periods; \(p\)-adic cohomologies; \(p\)-adic Galois representations PDFBibTeX XMLCite \textit{X. Caruso}, Panor. Synth. 54, 19--92 (2019; Zbl 1443.13018) Full Text: arXiv