Inter-universal geometry と ABC予想 (応援スレ) 45

[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 45 (1002ﾚｽ)
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27: 現代数学の系譜 雑談 ◆e.a0E5TtKE  [] 2020/05/04(月) 16:40:18 ID:ncpDqOGk

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https://en.wikipedia.org/wiki/P-adic_Hodge_theory
p-adic Hodge theory

In mathematics, p-adic Hodge theory is a theory that provides a way to classify and study p-adic Galois representations of characteristic 0 local fields[1] with residual characteristic p (such as Qp).
The theory has its beginnings in Jean-Pierre Serre and John Tate's study of Tate modules of abelian varieties and the notion of Hodge?Tate representation.
Hodge?Tate representations are related to certain decompositions of p-adic cohomology theories analogous to the Hodge decomposition, hence the name p-adic Hodge theory. Further developments were inspired by properties of p-adic Galois representations arising from the etale cohomology of varieties.
Jean-Marc Fontaine introduced many of the basic concepts of the field.

Contents
1 General classification of p-adic representations
2 Period rings and comparison isomorphisms in arithmetic geometry
3 Notes
4 References
4.1 Primary sources
4.2 Secondary sources

http://rio2016.5ch.net/test/read.cgi/math/1588552720/27

28: 現代数学の系譜 雑談 ◆e.a0E5TtKE  [] 2020/05/04(月) 16:48:52 ID:ncpDqOGk

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https://ja.wikipedia.org/wiki/%E3%82%A8%E3%82%BF%E3%83%BC%E3%83%AB%E5%B0%84
エタール射

エタール射（エタールしゃ、etale morphism）とは、数学において有限型スキーム間の平坦かつ不分岐な射のこと。
目次
1 不分岐
2 平坦
3 同値な定義
4 類体論と不分岐の対応

https://en.wikipedia.org/wiki/%C3%89tale_morphism
Etale morphism

In algebraic geometry, an etale morphism (French: [etal]) is a morphism of schemes that is formally etale and locally of finite presentation.
This is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology.
They satisfy the hypotheses of the implicit function theorem, but because open sets in the Zariski topology are so large, they are not necessarily local isomorphisms.
Despite this, etale maps retain many of the properties of local analytic isomorphisms, and are useful in defining the algebraic fundamental group and the etale topology.
The word etale is a French adjective, which means "slack", as in "slack tide", or, figuratively, calm, immobile, something left to settle.[1]

Contents
1 Definition
2 Examples
3 Properties
4 Inverse function theorem

http://rio2016.5ch.net/test/read.cgi/math/1588552720/28

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