Period Rings with Big Coefficients and Applications III

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.