p-adic Hodge theory for rigid-analytic varieties

Abstract

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-etale site, which makes all constructions completely functorial.

arXiv comment55 pages. Added result that connected affinoid rigid-analytic varieties over p-adic fields are K(pi,1)'s for p-torsion coefficients