翻訳と辞書 Words near each other ・ 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 ・ Quasi-foreign corporation ・ Quasi-Frobenius Lie algebra ・ Quasi-Frobenius ring ・ Quasi-Fuchsian group ・ Quasi-geostrophic equations ・ Quasi-harmonic approximation ・ Quasi-Hilda comet ・ Quasi-homogeneous polynomial ・ Quasi-Hopf algebra ・ Quasi-identifier ・ Quasi-invariant measure ・ Quasi-irreversible inhibitor ・ Quasi-isometry ・ Quasi-isomorphism 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-finite morphism ： ウィキペディア英語版 Quasi-finite morphism In algebraic geometry, a branch of mathematics, a morphism ''f'' : ''X'' → ''Y'' of schemes is quasi-finite if it is of finite type and satisfies any of the following equivalent conditions:〔EGA II, Définition 6.2.3〕 * Every point ''x'' of ''X'' is isolated in its fiber ''f''−1(''f''(''x'')). In other words, every fiber is a discrete (hence finite) set. * For every point ''x'' of ''X'', the scheme is a finite κ(''f''(''x'')) scheme. (Here κ(''p'') is the residue field at a point ''p''.) * For every point ''x'' of ''X'', $\backslash mathcal\_\backslash otimes\; \backslash kappa(f(x))$ is finitely generated over $\backslash kappa(f(x))$. Quasi-finite morphisms were originally defined by Alexander Grothendieck in SGA 1 and did not include the finite type hypothesis. This hypothesis was added to the definition in EGA II 6.2 because it makes it possible to give an algebraic characterization of quasi-finiteness in terms of stalks. For a general morphism and a point ''x'' in ''X'', ''f'' is said to be quasi-finite at ''x'' if there exist open affine neighborhoods ''U'' of ''x'' and ''V'' of ''f''(''x'') such that ''f''(''U'') is contained in ''V'' and such that the restriction is quasi-finite. ''f'' is locally quasi-finite if it is quasi-finite at every point in ''X''.〔EGA III, ErrIII, 20.〕 A quasi-compact locally quasi-finite morphism is quasi-finite. == Properties == For a morphism ''f'', the following properties are true.〔EGA II, Proposition 6.2.4.〕 * If ''f'' is quasi-finite, then the induced map ''f''red between reduced schemes is quasi-finite. * If ''f'' is a closed immersion, then ''f'' is quasi-finite. * If ''X'' is noetherian and ''f'' is an immersion, then ''f'' is quasi-finite. * If , and if is quasi-finite, then ''f'' is quasi-finite if any of the following are true: *#''g'' is separated, *#''X'' is noetherian, *# is locally noetherian. Quasi-finiteness is preserved by base change. The composite and fiber product of quasi-finite morphisms is quasi-finite.〔 If ''f'' is unramified at a point ''x'', then ''f'' is quasi-finite at ''x''. Conversely, if ''f'' is quasi-finite at ''x'', and if also $\backslash mathcal\_$, the local ring of ''x'' in the fiber ''f''−1(''f''(''x'')), is a field and a finite separable extension of κ(''f''(''x'')), then ''f'' is unramified at ''x''.〔EGA IV4, Théorème 17.4.1.〕 Finite morphisms are quasi-finite.〔EGA II, Corollaire 6.1.7.〕 A quasi-finite proper morphism locally of finite presentation is finite.〔EGA IV3, Théorème 8.11.1.〕 A generalized form of Zariski Main Theorem is the following:〔EGA IV3, Théorème 8.12.6.〕 Suppose ''Y'' is quasi-compact and quasi-separated. Let ''f'' be quasi-finite, separated and of finite presentation. Then ''f'' factors as $X\; \backslash hookrightarrow\; X\text{'}\; \backslash to\; Y$ where the first morphism is an open immersion and the second is finite. (''X'' is open in a finite scheme over ''Y''.) 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-finite 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.