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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Néron model ： ウィキペディア英語版 Néron model In algebraic geometry, the Néron model (or Néron minimal model, or minimal model) for an abelian variety ''AK'' defined over the field of fractions ''K'' of a Dedekind domain ''R'' is the "push-forward" of ''AK'' from Spec(''K'') to Spec(''R''), in other words the "best possible" group scheme ''AR'' defined over ''R'' corresponding to ''AK''. They were introduced by for abelian varieties over the quotient field of a Dedekind domain ''R'' with perfect residue fields, and extended this construction to semiabelian varieties over all Dedekind domains. ==Definition== Suppose that ''R'' is a Dedekind domain with field of fractions ''K'', and suppose that ''AK'' is a smooth separated scheme over ''K'' (such as an abelian variety). Then a Néron model of ''AK'' is defined to be a smooth separated scheme ''AR'' over ''R'' with fiber ''AK'' that is universal in the following sense. :If ''X'' is a smooth separated scheme over ''R'' then any ''K''-morphism from ''X''''K'' to ''AK'' can be extended to a unique ''R''-morphism from ''X'' to ''AR'' (Néron mapping property). In particular, the canonical map $A\_R(R)\backslash to\; A\_K(K)$ is an isomorphism. If a Néron model exists then it is unique up to unique isomorphism. In terms of sheaves, any scheme ''A'' over Spec(''K'') represents a sheaf for the flat Grothendieck topology, and this has a pushforward by the injection map from Spec(''K'') to Spec(''R''), which is a sheaf over Spec(''R''). If this pushforward is representable by a scheme, then this scheme is the Néron model of ''A''. In general the scheme ''AK'' need not have any Néron model. For abelian varieties ''AK'' Néron models exist and are unique (up to unique isomorphism) and are commutative quasi-projective group schemes over ''R''. The fiber of a Néron model over a closed point of Spec(''R'') is a smooth commutative algebraic group, but need not be an abelian variety: for example, it may be disconnected or a torus. Néron models exist as well for certain commutative groups other than abelian varieties such as tori, but these are only locally of finite type. Néron models do not exist for the additive group. 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「Néron model」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.