翻訳と辞書
Words near each other
・ Carter County, Montana
・ Carter County, Oklahoma
・ Carter County, Tennessee
・ Carter Covington
・ Carter Crest, Edmonton
・ Carter Cruise
・ Carter DeHaven
・ Carter Doctrine
・ Carter Dome
・ Carter Eckert
・ Carter Elliott
・ Carter F. Bales
・ Cartan's lemma
・ Cartan's lemma (potential theory)
・ Cartan's theorem
Cartan's theorems A and B
・ Cartanal
・ Cartanul River
・ Cartan–Brauer–Hua theorem
・ Cartan–Dieudonné theorem
・ Cartan–Eilenberg resolution
・ Cartan–Hadamard theorem
・ Cartan–Karlhede algorithm
・ Cartan–Kuranishi prolongation theorem
・ Cartan–Kähler theorem
・ Cartap
・ Cartas Chilenas
・ Cartas de amor
・ Cartas de amor (telenovela)
・ Cartas de Inglaterra


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

Cartan's theorems A and B : ウィキペディア英語版
Cartan's theorems A and B
In mathematics, Cartan's theorems A and B are two results proved by Henri Cartan around 1951, concerning a coherent sheaf on a Stein manifold . They are significant both as applied to several complex variables, and in the general development of sheaf cohomology.
:Theorem A. is spanned by its global sections.
Theorem B is stated in cohomological terms (a formulation that Cartan (1953, p.51) attributes to J.-P. Serre):
:Theorem B. for all .
Analogous properties were established by Serre (1955) for coherent sheaves in algebraic geometry, when is an affine scheme. The analogue of Theorem B in this context is as follows :
:Theorem B (Scheme theoretic analogue). Let be an affine scheme, a quasi-coherent sheaf of -modules for the Zariski topology on . Then for all .
These theorems have many important applications. Naively, they imply that a holomorphic function on a closed complex submanifold, , of a Stein manifold can be extended to a holomorphic function on all of . At a deeper level, these theorems were used by Jean-Pierre Serre to prove the GAGA theorem.
Theorem B is sharp in the sense that if for all coherent sheaves on a complex manifold (resp. quasi-coherent sheaves on a noetherian scheme ), then is Stein (resp. affine); see (resp. and ).
* See also Cousin problems
==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「Cartan's theorems A and B」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.