Mordell--Weil groups over large algebraic extensions of fields of characteristic zero
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914171541520384 |
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| author | Asayama, Takuya Taguchi, Yuichiro |
| author_facet | Asayama, Takuya Taguchi, Yuichiro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03495 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mordell--Weil groups over large algebraic extensions of fields of characteristic zero Asayama, Takuya Taguchi, Yuichiro Number Theory 12E30, 12F05, 14K15, 14G27 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. |
| title | Mordell--Weil groups over large algebraic extensions of fields of characteristic zero |
| topic | Number Theory 12E30, 12F05, 14K15, 14G27 |
| url | https://arxiv.org/abs/2408.03495 |