翻訳と辞書 Words near each other ・ Quasiperiodic motion ・ Quasiperiodic tiling ・ Quasiperiodicity ・ Quasipetalichthyidae ・ Quasipetalichthys ・ Quasiprobability distribution ・ Quasiregular ・ Quasiregular element ・ Quasiregular map ・ Quasiregular polyhedron ・ Quasiregular representation ・ Quasireversibility ・ Quasi-birth–death process ・ Quasi-category ・ Quasi-commutative property ・ Quasi-compact morphism ・ Quasi-constitutionality ・ Quasi-continuous function ・ Quasi-contract ・ Quasi-criminal ・ Quasi-crystals (supramolecular) ・ Quasi-delict ・ Quasi-derivative ・ Quasi-elemental ・ Quasi-empirical method ・ Quasi-empiricism in mathematics ・ Quasi-experiment ・ Quasi-fibration ・ Quasi-finite field ・ Quasi-finite morphism 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 Quasi-compact morphism ： ウィキペディア英語版 Quasi-compact morphism In algebraic geometry, a morphism $f:\; X\; \backslash to\; Y$ between schemes is said to be quasi-compact if ''Y'' can be covered by open affine subschemes $V\_i$ such that the pre-images $f^(V\_i)$ are quasi-compact (as topological space).〔This is the definition in Hartshorne.〕 If ''f'' is quasi-compact, then the pre-image of a quasi-compact open subscheme (e.g., open affine subscheme) under ''f'' is quasi-compact. It is not enough that ''Y'' admits a covering by quasi-compact open subschemes whose pre-images are quasi-compact. To give an example,〔Remark 1.5 in Vistoli〕 let ''A'' be a ring that does not satisfy the ascending chain conditions on radical ideals, and put $X\; =\; \backslash operatorname\; A$. ''X'' contains an open subset ''U'' that is not quasi-compact. Let ''Y'' be the scheme obtained by gluing two ''Xs along ''U''. ''X'', ''Y'' are both quasi-compact. If $f:\; X\; \backslash to\; Y$ is the inclusion of one of the copies of ''X'', then the pre-image of the other ''X'', open affine in ''Y'', is ''U'', not quasi-compact. Hence, ''f'' is not quasi-compact. A morphism from a quasi-compact scheme to an affine scheme is quasi-compact. Let $f:\; X\; \backslash to\; Y$ be a quasi-compact morphism between schemes. Then $f(X)$ is closed if and only if it is stable under specialization. The composition of quasi-compact morphisms is quasi-compact. The base change of a quasi-compact morphism is quasi-compact. An affine scheme is quasi-compact. In fact, a scheme is quasi-compact if and only if it is a finite union of open affine subschemes. Serre’s criterion gives a necessary and sufficient condition for a quasi-compact scheme to be affine. A quasi-compact scheme has at least one closed point.〔. See in particular Proposition 4.1.〕 == See also == *fpqc morphism 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「Quasi-compact morphism」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.