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An introduction to perfectoid spaces. (English) Zbl 1443.14022
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, 207-265 (2019).
Summary: The aim of these notes is to give a short introduction to P. Scholze’s theory of perfectoid spaces and their applications. These notes arise from a summer school “Perfectoid spaces” held in Bressanone (IT) from 31st August to 4th September 2015 in the framework of the Erasmus Mundus master programme ALGANT. The aim was to introduce perfectoid spaces to last year master students.
For the entire collection see [Zbl 1430.14001].
14F20 Étale and other Grothendieck topologies and (co)homologies
14F30 \(p\)-adic cohomology, crystalline cohomology
14G20 Local ground fields in algebraic geometry
14G22 Rigid analytic geometry
32P05 Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32-XX describing the type of problem)
14G45 Perfectoid spaces and mixed characteristic
14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry