New methods for?((arphi, Gamma))-modules

摘要

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 $$(arphi , Gamma )$$ ( φ , Γ ) -modules. These proofs are derived from joint work with Liu on relative p -adic Hodge theory, and are closely related to the theory of perfectoid algebras and spaces, as in the work of Scholze.