翻訳と辞書 Words near each other ・ Grotesque dance ・ Grotesque Impalement ・ Grotesque Wedlock ・ Grotesquerie ・ Groth ・ Grothe ・ Grothendieck category ・ Grothendieck connection ・ Grothendieck construction ・ Grothendieck duality ・ Grothendieck existence theorem ・ Grothendieck group ・ Grothendieck inequality ・ Grothendieck local duality ・ Grothendieck space ・ Grothendieck spectral sequence ・ Grothendieck topology ・ Grothendieck trace formula ・ Grothendieck universe ・ Grothendieck's connectedness theorem ・ Grothendieck's Galois theory ・ Grothendieck's relative point of view ・ Grothendieck's Tôhoku paper ・ Grothendieck–Katz p-curvature conjecture ・ Grothendieck–Ogg–Shafarevich formula ・ Grothendieck–Riemann–Roch theorem ・ Grothendieck–Teichmüller group ・ Grothusenkoog ・ Grotius Lectures ・ Grotius Society Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Grothendieck spectral sequence ： ウィキペディア英語版 Grothendieck spectral sequence In mathematics, in the field of homological algebra, the Grothendieck spectral sequence, introduced in ''Tôhoku paper'', is a spectral sequence that computes the derived functors of the composition of two functors $G\backslash circ\; F$, from knowledge of the derived functors of ''F'' and ''G''. If $F\; :\backslash mathcal\backslash to\backslash mathcal$ and $G\; :\backslash mathcal\backslash to\backslash mathcal$ are two additive and left exact functors between abelian categories such that $F$ takes ''F''-acyclic objects (e.g., injective objects) to $G$-acyclic objects and if $\backslash mathcal$ has enough injectives, then there is a spectral sequence for each object $A$ of $\backslash mathcal$ that admits an ''F''-acyclic resolution: :$E\_2^\; =\; (^p\; G\; \backslash circ^q\; F)(A)\; \backslash Longrightarrow\; ^\; (G\backslash circ\; F)(A).$ Many spectral sequences in algebraic geometry are instances of the Grothendieck spectral sequence, for example the Leray spectral sequence. The exact sequence of low degrees reads :0 → ''R''1''G''(''FA'') → ''R''1(''GF'')(''A'') → ''G''(''R''1''F''(''A'')) → ''R''2''G''(''FA'') → ''R''2(''GF'')(''A''). == Examples == 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「Grothendieck spectral sequence」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.