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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 Iwasawa theory ： ウィキペディア英語版 Iwasawa theory In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by , as part of the theory of cyclotomic fields. In the early 1970s, Barry Mazur considered generalizations of Iwasawa theory to abelian varieties. More recently (early 90s), Ralph Greenberg has proposed an Iwasawa theory for motives. ==Formulation== Iwasawa worked with so-called $\backslash mathbb\_p$-extensions: infinite extensions of a number field $F$ with Galois group $\backslash Gamma$ isomorphic to the additive group of p-adic integers for some prime ''p''. Every closed subgroup of $\backslash Gamma$ is of the form $\backslash Gamma^$, so by Galois theory, a $\backslash mathbb\_p$-extension $F\_\backslash infty/F$ is the same thing as a tower of fields $F\; =\; F\_0\; \backslash subset\; F\_1\; \backslash subset\; F\_2\; \backslash subset\; \backslash ldots\; \backslash subset\; F\_\backslash infty$ such that $\backslash textrm(F\_n/F)\backslash cong\; \backslash mathbb/p^n\backslash mathbb$. Iwasawa studied classical Galois modules over $F\_n$ by asking questions about the structure of modules over $F\_\backslash infty$. More generally, Iwasawa theory asks questions about the structure of Galois modules over extensions with Galois group a p-adic Lie group. 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「Iwasawa 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.