p-adic Hodge theory for rigid-analytic varieties

TL;DR

This paper establishes de Rham comparison isomorphisms for rigid-analytic varieties using perfectoid spaces and the pro-étale site, advancing p-adic Hodge theory in a functorial framework.

Contribution

It provides new proofs of de Rham comparison isomorphisms for rigid-analytic varieties incorporating coefficients and families, utilizing perfectoid spaces and the pro-étale site.

Findings

Proofs of de Rham comparison isomorphisms for rigid-analytic varieties.

Introduction of the pro-étale site for functorial constructions.

Extension of p-adic Hodge theory techniques to families and coefficients.

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.