[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(1): 現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/05/04(月)16:40 ID:ncpDqOGk(20/40) AAS
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外部ﾘﾝｸ:en.wikipedia.org
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

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