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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 Parshin's conjecture ： ウィキペディア英語版 Parshin's conjecture In mathematics, more specifically in algebraic geometry, Parshin's conjecture (also referred to as the Beilinson–Parshin conjecture) states that for any smooth projective variety ''X'' defined over a finite field, the higher algebraic K-groups vanish up to torsion: :$K\_i(X)\; \backslash otimes\; \backslash mathbf\; Q\; =\; 0\; \backslash \; \backslash ,\; i\; >\; 0.$ It is named after Aleksei Nikolaevich Parshin and Alexander Beilinson. ==Points and curves== The conjecture holds for a finite field by Quillen's computations of the ''K''-groups in this case. Secondly, for a smooth proper curve, Quillen〔see 〕 has shown that the ''K''-groups are finitely generated, while Harder's computations show that the groups are torsion. The two results together thus show Parshin's conjecture for curves. 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「Parshin's conjecture」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.