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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2510.24588 |
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| _version_ | 1866911574149562368 |
|---|---|
| author | Huryn, Jake |
| author_facet | Huryn, Jake |
| contents | Let $K$ be a number field, and let $A$ be an Abelian variety over $K$ which has no CM isogeny-factors over $\overline{K}$. We prove that $A$ has only finitely many torsion points over the maximal $n$-step-solvable extension of $K$ for any $n$ and only finitely many torsion points of prime order over the maximal prosolvable extension of $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24588 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Torsion of Abelian varieties over solvable extensions of number fields Huryn, Jake Number Theory 11G10, 14G27, 14K15 Let $K$ be a number field, and let $A$ be an Abelian variety over $K$ which has no CM isogeny-factors over $\overline{K}$. We prove that $A$ has only finitely many torsion points over the maximal $n$-step-solvable extension of $K$ for any $n$ and only finitely many torsion points of prime order over the maximal prosolvable extension of $K$. |
| title | Torsion of Abelian varieties over solvable extensions of number fields |
| topic | Number Theory 11G10, 14G27, 14K15 |
| url | https://arxiv.org/abs/2510.24588 |