Forum of Mathematics, Pi (Jan 2013)

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

  • PETER SCHOLZE

DOI
https://doi.org/10.1017/fmp.2013.1
Journal volume & issue
Vol. 1

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.

Keywords