翻訳と辞書 Words near each other ・ Bocking's Elm ・ Bockkarkopf ・ Bockleton ・ Bockman ・ Bockmer End ・ Bockrath ・ Bockris ・ Bocksberg (Harz) ・ Bocksbeutel ・ Bockscar ・ Bocksdorf ・ Bockstadt ・ Bockstael metro station ・ Bockstael railway station ・ Bockstein homomorphism ・ Bockstein spectral sequence ・ Bocksten Man ・ Bocktenhorn ・ Bocktschingel ・ Bockum ・ Bockwurst ・ Boclair Academy ・ BOclassic ・ Boclod ・ BOCM ・ BOCM Pauls ・ Boco ・ Boco River ・ Boco, Les Anglais, Haiti ・ Bocoa 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 Bockstein spectral sequence ： ウィキペディア英語版 Bockstein spectral sequence In mathematics, the Bockstein spectral sequence is a spectral sequence relating the homology with mod ''p'' coefficients and the homology reduced mod ''p''. It is named after Meyer Bockstein. == Definition == Let ''C'' be a chain complex of torsion-free abelian groups and ''p'' a prime number. Then we have the exact sequence: :$0\; \backslash to\; C\; \backslash overset\backslash to\; C\; \backslash overset\backslash to\; C\; \backslash otimes\; \backslash mathbb/p\; \backslash to\; 0$. Taking integral homology ''H'', we get the exact couple of "doubly graded" abelian groups: :$H\_$ *(C) \overset\to H_ *(C) \overset \to H_ *(C \otimes \mathbb/p) \overset \to . where the grading goes: $H\_$ *(C)_ = H_(C) and the same for $H\_$ *(C \otimes \mathbb/p), $\backslash operatorname\; i\; =\; (1,\; -1)$, $\backslash operatorname\; j\; =\; (0,\; 0)$, $\backslash operatorname\; k\; =\; (-1,\; 0)$. This gives the first page of the spectral sequence: we take $E\_^1\; =\; H\_(C\; \backslash otimes\; \backslash mathbb/p)$ with the differential $\backslash to\; D^r\; \backslash overset$ and $\backslash operatorname\; \backslash to\; \backslash mathbb\; \backslash to\; \backslash mathbb/p\; \backslash to\; 0$, we get: :$0\; \backslash to\; \backslash operatorname\_1^/p)\; \backslash to\; D\_n^r\; \backslash overset\backslash to\; D\_n^r\; \backslash to\; D\_n^r\; \backslash otimes\; \backslash mathbb/p\; \backslash to\; 0$. This tells the kernel and cokernel of $D^r\_n\; \backslash overset\backslash to\; D^r\_n$. Expanding the exact couple into a long exact sequence, we get: for any ''r'', :$0\; \backslash to\; (p^\; H\_n(C))\; \backslash otimes\; \backslash mathbb/p\; \backslash to\; E^r\_\; \backslash to\; \backslash operatorname(p^\; H\_(C),\; \backslash mathbb/p)\; \backslash to\; 0$. When $r\; =\; 1$, this is the same thing as the universal coefficient theorem for homology. Assume the abelian group $H\_$ *(C) is finitely generated; in particular, only finitely many cyclic modules of the form $\backslash mathbb/p^s$ can appear as a direct summand of $H\_$ *(C). Letting $r\; \backslash to\; \backslash infty$ we thus see $E^\backslash infty$ is isomorphic to $(\backslash text\; H\_$ *(C)) \otimes \mathbb/p. 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「Bockstein 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.