[過去ﾛｸﾞ] 現代数学の系譜 工学物理雑談 古典ガロア理論も読む79 (1002ﾚｽ)
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182(1): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE 2019/11/27(水)07:49 ID:qnEhNItW(1/3) AAS
>>181

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Contents
1 General classification of p-adic representations
2 Period rings and comparison isomorphisms in arithmetic geometry

General classification of p-adic representations
Let K be a local field with residue field k of characteristic p. In this article, a p-adic representation of K (or of GK, the absolute Galois group of K) will be a continuous representation ρ : GK→ GL(V), where V is a finite-dimensional vector space over Qp.
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183: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE 2019/11/27(水)07:50 ID:qnEhNItW(2/3) AAS
>>182

つづき

Period rings and comparison isomorphisms in arithmetic geometry
The general strategy of p-adic Hodge theory, introduced by Fontaine, is to construct certain so-called period rings[3] such as BdR, Bst, Bcris, and BHT which have both an action by GK and some linear algebraic structure and to consider so-called Dieudonne modules

D_{B}(V)=(B\otimes _{\mathbf {Q} _{p}}V)^{G_{K}}}
(where B is a period ring, and V is a p-adic representation) which no longer have a GK-action, but are endowed with linear algebraic structures inherited from the ring B.
In particular, they are vector spaces over the fixed field E:=B^{G_{K}}}E:=B^{{G_{K}}}.[4] This construction fits into the formalism of B-admissible representations introduced by Fontaine.
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