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

2024/08/07 by Takuya Asayama, Asayama, Takuya, Yuichiro Taguchi +1 · 1 citation
Mathematics · Physics and Astronomy · #12E30 #12F05 #14G27 #14K15 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2408.03495

openalex publication_date 2024/08/07 · openalex created_date 2024/11/01 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Kummer-faithfulness over p-adic fields

Related

• Kummer-faithfulness for function fields
• On Mordell-Weil groups of Jacobians over function fields
• A Mordell-Weil theorem for abelian varieties over fields generated by torsion points
• Kummer-faithfulness over p-adic fields
• On Mordell-Weil group of isotrivial abelian varieties over function fields