Abstract
We provide new proofs of two key results of p-adic Hodge theory: the Fontaine-Wintenberger isomorphism between Galois groups in characteristic 0 and characteristic p, and the Cherbonnier-Colmez theorem on decompletion of (phi, Gamma)-modules. These proofs are derived from joint work with Liu on relative p-adic Hodge theory, and are closely related to Scholze's study of perfectoid algebras and spaces.
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