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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク P-adic Hodge theory ： ウィキペディア英語版 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〔In this article, a ''local field'' is complete discrete valuation field whose residue field is perfect.〕 with residual characteristic ''p'' (such as Q''p''). 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 étale cohomology of varieties. Jean-Marc Fontaine introduced many of the basic concepts of the field. ==General classification of ''p''-adic representations== Let ''K'' be a local field of 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 Q''p''. The collection of all ''p''-adic representations of ''K'' form an abelian category denoted $\backslash mathrm\_(K)$ in this article. ''p''-adic Hodge theory provides subcollections of ''p''-adic representations based on how nice they are, and also provides faithful functors to categories of linear algebraic objects that are easier to study. The basic classification is as follows: :$\backslash mathrm\_(K)\backslash subsetneq\backslash mathrm\_(K)\backslash subsetneq\; \backslash mathrm\_(K)\backslash subsetneq\; \backslash mathrm\_(K)\backslash subsetneq\; \backslash mathrm\_(K)$ where each collection is a full subcategory properly contained in the next. In order, these are the categories of crystalline representations, semistable representations, de Rham representations, Hodge–Tate representations, and all ''p''-adic representations. In addition, two other categories of representations can be introduced, the potentially crystalline representations Reppcris(''K'') and the potentially semistable representations Reppst(''K''). The latter strictly contains the former which in turn generally strictly contains Repcris(''K''); additionally, Reppst(''K'') generally strictly contains Repst(''K''), and is contained in RepdR(''K'') (with equality when the residue field of ''K'' is finite, a statement called the ''p''-adic monodromy theorem). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「P-adic Hodge theory」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.