Torsion of rank-two $A$-motives values in odd characteristic cyclotomic towers
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908487470022656 |
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| author | Okumura, Yoshiaki |
| author_facet | Okumura, Yoshiaki |
| contents | For rank-two $A$-motives defined over local fields with odd characteristic, we give an analogue of a theorem of Imai stating that abelian varieties with good reduction over $p$-adic fields have only finitely many torsion points values in cyclotomic towers. This implies the finiteness of torsion points of abelian Anderson $A$-modules. For rank-two Drinfeld $A$-modules over global function fields, we also give an analogue of a theorem of Ribet on torsion points of abelian varieties values in maximal cyclotomic extensions of number fields. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_08692 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Torsion of rank-two $A$-motives values in odd characteristic cyclotomic towers Okumura, Yoshiaki Number Theory Primary 11G09, 11R58, Secondary 11F80, 14G05 For rank-two $A$-motives defined over local fields with odd characteristic, we give an analogue of a theorem of Imai stating that abelian varieties with good reduction over $p$-adic fields have only finitely many torsion points values in cyclotomic towers. This implies the finiteness of torsion points of abelian Anderson $A$-modules. For rank-two Drinfeld $A$-modules over global function fields, we also give an analogue of a theorem of Ribet on torsion points of abelian varieties values in maximal cyclotomic extensions of number fields. |
| title | Torsion of rank-two $A$-motives values in odd characteristic cyclotomic towers |
| topic | Number Theory Primary 11G09, 11R58, Secondary 11F80, 14G05 |
| url | https://arxiv.org/abs/2508.08692 |