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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 $$(\varphi , \Gamma )$$ ( 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

New methods for $$(\varphi, \Gamma)$$ ( φ , Γ ) -modules

Research in the Mathematical Sciences , Volume 2 (1) – Oct 16, 2015

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References (16)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Kedlaya.
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis
eISSN
2197-9847
DOI
10.1186/s40687-015-0031-z
Publisher site
See Article on Publisher Site

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 $$(\varphi , \Gamma )$$ ( 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.

Journal

Research in the Mathematical SciencesSpringer Journals

Published: Oct 16, 2015

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