Explicit bounds on torsion of CM abelian varieties over $p$-adic fields with values in Lubin-Tate extensions
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arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917730528002048 |
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| author | Ozeki, Yoshiyasu |
| author_facet | Ozeki, Yoshiyasu |
| contents | 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 $L=K(μ_{p^{\infty}})$). 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_13725 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Explicit bounds on torsion of CM abelian varieties over $p$-adic fields with values in Lubin-Tate extensions Ozeki, Yoshiyasu Number Theory 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 $L=K(μ_{p^{\infty}})$). 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. |
| title | Explicit bounds on torsion of CM abelian varieties over $p$-adic fields with values in Lubin-Tate extensions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2303.13725 |