Explicit bounds on torsion of CM abelian varieties over $p$-adic fields with values in Lubin-Tate extensions
| Autor: | Ozeki, Yoshiyasu |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Pacific J. Math. 330 (2024) 171-197 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/pjm.2024.330.171 |
| Popis: | Let $K$ and $k$ be $p$-adic fields. Let $L$ be the composite field of $K$ and a certain Lubin-Tate extension over $k$ (including the case where $L=K(\mu_{p^{\infty}})$). In this paper, we show that there exists an explicitly described constant $C$, depending only on $K,k$ and an integer $g \ge 1$, which satisfies the following property: If $A_{/K}$ is a $g$-dimensional CM abelian variety, then the order of the $p$-torsion subgroup of $A(L)$ is bounded by $C$. We also give a similar bound in the case where $L=K(\sqrt[p^{\infty}]{K})$. Applying our results, we study bounds of orders of torsion subgroups of some CM abelian varieties over number fields with values in full cyclotomic fields. Comment: 21 pages, some minor modifications |
| Databáze: | arXiv |
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