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Title
Japanese:On the structure of Mordell–Weil groups over large algebraic extensions 
English:On the structure of Mordell–Weil groups over large algebraic extensions 
Author
Japanese: 浅山拓哉.  
English: Takuya Asayama.  
Language Japanese 
Journal/Book name
Japanese:数理解析研究所講究録 
English:RIMS Kôkyûroku 
Volume, Number, Page vol. 2332        pp. 133–143
Published date Jan. 2026 
Publisher
Japanese:京都大学数理解析研究所 
English:Research Institute for Mathematical Sciences, Kyoto University 
Conference name
Japanese:代数学的整数論とその周辺 
English:Algebraic Number Theory and Related Topics 
Conference site
Japanese:京都府 
English:Kyoto 
Abstract This note provides some previous works and our recent results on the structure of the Mordell–Weil groups of semiabelian varieties over certain infinite algebraic extensions of finitely generated fields over the field of rational numbers. We deal with two types of algebraic extensions; the first one is of extensions obtained by adjoining the coordinates of certain points of various semiabelian varieties; the second one is of extensions that arise as the fixed subfield in the algebraically closed field by a finite number of field automorphisms. We show that some of these fields are not sub-p-adic, but become new examples of Kummer-faithful fields, which are expected to be suitable as ground fields of anabelian geometry. Moreover, both cases can occur, in which the Mordell–Weil groups modulo torsion over these fields are free of infinite rank and not free. This note is based on joint work with Yuichiro Taguchi (Institute of Science Tokyo) and on the author's talk at the RIMS Workshop ``Algebraic Number Theory and Related Topics" held in January 2025.

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