Period Rings with Big Coefficients and Applications III

TL;DR

This paper advances the theory of period rings with large coefficients, focusing on noncommutative descent in the pro-étale topology within p-adic Hodge theory and noncommutative geometry.

Contribution

It extends noncommutative descent from étale to pro-étale topology in both Tate and analytic contexts, enriching the framework of p-adic Hodge theory.

Findings

Extended noncommutative descent to pro-étale topology

Applied to p-adic Hodge theory and noncommutative geometry

Enhanced understanding of period rings with big coefficients

Abstract

We continue our study on the corresponding period rings with big coefficients, with the corresponding application in mind on relative $p$-adic Hodge theory and noncommutative analytic geometry. In this article, we extend the discussion of the corresponding noncommutative descent over \'etale topology to the corresponding noncommutative descent over pro-\'etale topology in both Tate and analytic setting.