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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 Beilinson regulator ： ウィキペディア英語版 Beilinson regulator In mathematics, especially in algebraic geometry, the Beilinson regulator is the Chern class map from algebraic K-theory to Deligne cohomology: :$K\_n\; (X)\; \backslash rightarrow\; \backslash oplus\_\; H\_D^\; (X,\; \backslash mathbf\; Q(p)).$ Here, ''X'' is a complex smooth projective variety, for example. It is named after Alexander Beilinson. The Beilinson regulator features in Beilinson's conjecture on special values of L-functions. The ''Dirichlet regulator'' map (used in the proof of Dirichlet's unit theorem) for the ring of integers $\backslash mathcal\; O\_F$ of a number field ''F'' :$\backslash mathcal\; O\_F^\backslash times\; \backslash rightarrow\; \backslash mathbf\; R^,\; \backslash \; \backslash \; x\; \backslash mapsto\; (\backslash log\; |\backslash sigma\; (x)|)\_\backslash sigma$ is a particular case of the Beilinson regulator. (As usual, $\backslash sigma:\; F\; \backslash subset\; \backslash mathbf\; C$ runs over all complex embeddings of ''F'', where conjugate embeddings are considered equivalent.) Up to a factor 2, the Beilinson regulator is also generalization of the Borel regulator. == References == * 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「Beilinson regulator」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.