Abelian Varieties
Abelian Varieties
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DOI：
10.1007/978-1-4612-0041-3_6
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发表时间：
2021-10
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影响因子：
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通讯作者：
Caleb Ji
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文献类型：
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作者：
Caleb Ji
在第一部分中，我们简要回顾了c上复解析环面与阿贝尔变分之间的关系，然后介绍了非阿基米德值域k上解析环面T的乘法模拟。研究了具有特征群X (T)的代数环面T / k的解析结构Tan，以及格A c Tan和解析环面T= Tan I A的结构。对于T上的解析线束，这里用自同构因子Z表示，计算了全局截面L (Z)的向量空间维数。当且仅当黎曼形式a: a -+ X (T)存在时，证明解析环面T是一个阿贝尔变分的解析。最后，概述了Neron模型的理论和k上一般阿贝尔变的均匀化。本章中介绍的结果是许多作者的工作，A. Grothendieck， M. Raynaud， D. Mumford， L. Gerritzen， Y. Manin， V. Drinfeld， S. Bosch， W. Liitkebohmert等人。
In the first section, we briefly recall the relation between complex analytic tori and abelian varieties over C. Then the multiplicative analogue of an analytic torus T over a non-archimedean valued field k is introduced. The analytic structure of the analytification Tan of an algebraic torus T over k, with character group X (T), is investigated, as well as lattices A c Tan and the structure of the analytic torus T= Tan I A. For analytic line bundles on T, here represented by automorphy factors Z, the dimension of the vector space of global sections L (Z) is calculated. This information leads to a proof that the analytic torus T is the analytification of an abelian variety if and only if a Riemann form a: A-+ X (T) exists. Finally, the theory of Neron models and the uniformization of general abelian varieties over k is sketched. The results, presented in this chapter, are the work of many authors, A. Grothendieck, M. Raynaud, D. Mumford, L. Gerritzen, Y. Manin, V. Drinfeld, S. Bosch, W. Liitkebohmert et al.