記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer Science and Business Media LLC  

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.

DOI： 10.1007/s40993-025-00658-2

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その他リンク： https://link.springer.com/article/10.1007/s40993-025-00658-2/fulltext.html

記述言語：日本語   掲載種別：研究論文（学術雑誌）  

DOI： 10.14943/J.HighEdu.32.47

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Mathematical Institute, Tohoku University  

In this paper, we study the ramification of extensions of a function field generated by division points of rank 2 Drinfeld modules. Also conductors of certain rank 2 Drinfeld modules are defined as analogues of those for elliptic curves. A calculation of these conductors allows us to show an analogue of Szpiro's conjecture under a certain limited situation.

DOI： 10.2748/tmj.20230224

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Elsevier  

Geyer and Jarden proved several results for torsion points of elliptic curves defined over the fixed field by finitely many elements in the absolute Galois group of a finitely generated field over the prime field in its algebraic closure. As an analogue of these results, this paper studies torsion points of Drinfeld modules defined over the fixed field by finitely many elements in the absolute Galois group of a finitely generated function field in its algebraic closure. We prove some results which are similar to those of Geyer and Jarden.

DOI： 10.1016/j.jnt.2021.03.014

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開催年月日： 2026年3月

記述言語：日本語   会議種別：口頭発表（一般）  

開催地：山梨大学  

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開催年月日： 2025年9月

記述言語：日本語   会議種別：口頭発表（一般）  

開催地：神奈川大学  

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開催年月日： 2025年1月

記述言語：日本語   会議種別：口頭発表（一般）  

開催地：京都大学数理解析研究所  

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開催年月日： 2024年12月

記述言語：日本語   会議種別：口頭発表（一般）  

開催地：岩手県立大学  

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開催年月日： 2024年7月

記述言語：日本語   会議種別：口頭発表（一般）  

開催地：東北大学  

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