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Title
Japanese: 
English:Mordell–Weil groups over large algebraic extensions of fields of characteristic zero 
Author
Japanese: 浅山 拓哉, 田口 雄一郎.  
English: Takuya Asayama, Yuichiro Taguchi.  
Language English 
Journal/Book name
Japanese: 
English:Research in Number Theory 
Volume, Number, Page Vol. 11    Issue 4   
Published date Sept. 11, 2025 
Publisher
Japanese: 
English: 
Conference name
Japanese: 
English: 
Conference site
Japanese: 
English: 
DOI https://doi.org/10.1007/s40993-025-00658-2
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.

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