Geodesic
$p$-ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES
Forum of Mathematics, Pi, Tome 1 (2013)

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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. 
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PETER SCHOLZE. $p$-ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES. Forum of Mathematics, Pi, Tome 1 (2013). doi: 10.1017/fmp.2013.1

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