标题： Mordell--Weil群在特征为零的域的大代数扩张上 显示英文标题

标题： Mordell--Weil groups over large algebraic extensions of fields of characteristic zero

摘要： 我们研究了在特征为零的有限生成域的大代数扩张上的半阿贝尔簇的Mordell--Weil群的结构。 我们在本文中考虑了两种类型的代数扩张；一种是通过附加各种半阿贝尔簇的某些点的坐标得到的扩张；另一种是通过有限多个自同构在代数闭域中的固定子域得到的扩张。 其中一些域被证明是新的Kummer忠实域，这些域不是子$p$-有理域。 在其中，我们找到了既存在模扭群为无限秩自由的Kummer忠实域，也存在模扭群不自由的Kummer忠实域的例子。 显示英文摘要

摘要： We study the structure of the Mordell--Weil groups of semiabelian varieties over large algebraic extensions of a finitely generated field of characteristic zero. We consider two types of algebraic extensions in this paper; one is of extensions obtained by adjoining the coordinates of certain points of various semiabelian varieties; the other is of extensions obtained as the fixed subfield in an algebraically closed field by a finite number of automorphisms. Some of such fields turn out to be new examples of Kummer-faithful fields which are not sub-$p$-adic. Among them, we find both examples of Kummer-faithful fields over which the Mordell--Weil group modulo torsion can be free of infinite rank and not free.