New methods for \((\varphi, \Gamma)\) -modules

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• 作者：Kiran S Kedlaya
• 关键词：p ; adic Hodge theory ; Perfectoid fields ; Field of norms equivalence ; Witt vectors ; \((\varphi ; \Gamma )\) ; modules ; Cherbonnier–Colmez theorem
• 刊名：Research in the Mathematical Sciences
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2
• 期：1
• 全文大小：2,987 KB
• 刊物类别：Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis;
• 刊物主题：Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis;
• 出版者：Springer International Publishing
• ISSN：2197-9847

文摘

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, and are closely related to the theory of perfectoid algebras and spaces, as in the work of Scholze.