Torsion of rank-two $A$-motives values in odd characteristic cyclotomic towers

Yoshiaki Okumura

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arXiv · 2508.08692

Torsion of rank-two $A$-motives values in odd characteristic cyclotomic towers

Yoshiaki Okumura

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Abstract

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.

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Yoshiaki Okumura. 2025-08-12. Torsion of rank-two $A$-motives values in odd characteristic cyclotomic towers. https://arxiv.org/abs/2508.08692

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