New methods for $$(\varphi, \Gamma)$$ ( φ , Γ ) -modules
New methods for $$(\varphi, \Gamma)$$ ( φ , Γ ) -modules
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 $$(\varphi , \Gamma )$$ -modules. These proofs are derived from joint work with Liu on relative p-adic Hodge theory, …