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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 Hochster–Roberts theorem ： ウィキペディア英語版 Hochster–Roberts theorem In algebra, the Hochster–Roberts theorem, introduced by , states that rings of invariants of reductive groups acting on regular rings are Cohen–Macaulay. In other words, :If ''V'' is a rational representation of a reductive group ''G'' over a field ''k'', then there exist algebraically independent invariant homogeneous polynomials $f\_1,\; \backslash cdots,\; f\_d$ such that $k()^G$ is a free finite graded module over $k(\backslash cdots,\; f\_d)$. proved that if a variety has rational singularities then so does its quotient by the action of a reductive group; this implies the Hochster–Roberts theorem as rational singularities are Cohen–Macaulay. == References == * * * Mumford, D.; Fogarty, J.; Kirwan, F. ''Geometric invariant theory''. Third edition. Ergebnisse der Mathematik und ihrer Grenzgebiete (2) (Results in Mathematics and Related Areas (2)), 34. Springer-Verlag, Berlin, 1994. xiv+292 pp. ISBN 3-540-56963-4 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「Hochster–Roberts theorem」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.