Perfectoid spaces

2011/11/21 by Scholze, Peter · 7 citations
#11S15 #12J25 #14G10 #14G17 #14G20 #14G22 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1111.4914

Abstract

We introduce a certain class of so-called perfectoid rings and spaces, which give a natural framework for Faltings' almost purity theorem, and for which there is a natural tilting operation which exchanges characteristic 0 and characteristic p. We deduce the weight-monodromy conjecture in certain cases by reduction to equal characteristic.

Cited by

• Model theory of tame valued fields and beyond: recent developments and open questions
• Graded perfectoid rings
• A Weight Structure on Rigid Analytic Motives over a Field
• Almost Noetherian rings and modules
• A motivic approach to rational p-adic cohomologies
• Perfectoid Spaces in Multivariate p-adic Hodge Theory
• Banach modules, almost mathematics and condensed mathematics

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