Explicit bounds on torsion of CM abelian varieties over \(p\)-adic fields with values in Lubin-Tate extensions
type: Item
instance of: scholarly article
title: Explicit bounds on torsion of CM abelian varieties over \(p\)-adic fields with values in Lubin-Tate extensions
author: Yoshiyasu Ozeki
published in: Pacific Journal of Mathematics
publication date: 2024-07-29T00:00:00Z
review text: 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 \(L = K(\mu_{p^{\infty}})\)). The author shows that there exists an explicitly described constant \(C\), depending only on \(K\), \(k\) and an integer \(g \geq 1\), which satisfies the following property: if \(A/K\) is a \(g\)-dimensional \(CM\) abelian variety, then the order of the \(p\)-primary torsion subgroup of \(A(L)\) is bounded by \(C\) (Theorem 3.1). Similar bound is given in the case where \(L = K(K^{1/p^{\infty}})\). Main results are next applied to study bounds of orders of torsion subgroups of some \(CM\) abelian varieties over number fields with values in full cyclotomic fields (Theorem 1.3).
reviewed by: Andrzej Dąbrowski
Mathematics Subject Classification ID: 11G10
zbMATH DE Number: 7887958
zbMATH Keywords: abelian varieties
zbMATH Keywords: Lubin-Tate extensions
MaRDI profile type: Publication
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DOI: 10.2140/PJM.2024.330.171
description: scientific article; zbMATH DE number 7887958