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<p>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-<i>p</i>-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.</p>

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Mordell–Weil groups over large algebraic extensions of fields of characteristic zero

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  • 发表日期：

    2025年9月11日

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  • Takuya Asayama,
  • Yuichiro Taguchi

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.