Non Commutative Geometry I
Non Commutative Geometry I
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发表时间：
2017-04
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通讯作者：
Kazuhisa Maehara;General Education
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作者：
Kazuhisa Maehara;General Education
本文介绍了Kontsevich和Rosenberg提出的一种非交换代数几何([Kon]，[MCH])，并用最近发展起来的核心和余模理论([Brz])来表示。利用有限群([AM]，[BJ]，[Breen1]，[Breen2]，[Gir]，[SGA]，[S1]，[S2]，[Shatz]，[Se]，[Zuo]，[RBZL])，我们将自己局限于非对易代数簇范畴，并利用无限伽罗华体理论发展了双曲几何。我们将它应用于后面定义的特征为0的域([Iita]，[Fuj]，[Kaw]，[Mats]，[MP]，[Km~3])上的一般类型的非对易簇。射影簇([Iita]，[Mum]，[Vieh]，[Ko1]，[Zuo])的主要分类工具是所谓的特征p>；0技巧([MP]，[Ko2]，[BBD]，[Bberth])和纤维空间的多次方对偶层的弱正向映象([Kaw]，[Ws]，[Vieh]，[Nak]，[Km1])以及Kawamata-Viehweg消失定理([MP])。我们使用的不是这些工具，而是无限群。
In this article we shall introduce a non commutative algebraic geometry by Kontsevich and Rosenberg([Kon], [Mch]) and represent it by recently develoved theory of corings and comodules([Brz]). We restrict ourselves to the category of non commutative algebraic varieties and develope the birational geometry by infinite Galois theory of skew fields making use of profinite groups([AM],[BJ],[Breen1],[Breen2],[Gir], [SGA], [S1], [S2], [Shatz], [Se], [Zuo], [RBZL]). We apply it to non commutative varieties of general type defined later over the field of characteristic 0([Iita], [Fuj], [Kaw], [Mats], [MP], [Km3]). Main tools of classification of projective varieties([Iita], [Mum], [Vieh], [Ko1], [Zuo]) are so called characteristic p > 0 technic([MP], [Ko2]), [BBD], [Berth]) and weak positivity direct images of multi-power of dualizing sheaves for fibre spaces([Kaw], [Ws], [Vieh], [Nak], [Km1]) as well as Kawamata-Viehweg vanishing theorems([MP]). Instead of these tools, we make use of profinite groups.