Period Rings with Big Coefficients and Applications III

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 étale topology to the corresponding noncommutative descent over pro-étale topology in both Tate and analytic setting.

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