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$p$-ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES

Part of: Arithmetic problems. Diophantine geometry Cycles and subschemes Compact analytic spaces

Published online by Cambridge University Press:  17 May 2013

PETER SCHOLZE
PETER SCHOLZE*
Affiliation:
Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, [email protected]

Abstract

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We give proofs of de Rham comparison isomorphisms for rigid-analytic varieties, with coefficients and in families. This relies on the theory of perfectoid spaces. Another new ingredient is the pro-étale site, which makes all constructions completely functorial.

MSC classification

Secondary: 14G22: Rigid analytic geometry 14C30: Transcendental methods, Hodge theory , Hodge conjecture 14G20: Local ground fields 32J27: Compact Kähler manifolds
Type
Research Article
Information
Forum of Mathematics, Pi , Volume 1 , 2013 , e1
Creative Commons
Creative Common License - CCCreative Common License - BY
The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence .
Copyright
© The Author(s) 2013.

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