Bounds on torsion of CM abelian varieties over a \(p\)-adic field with values in a field of \(p\)-power roots

arXiv2209.01811MaRDI QIDQ6127274

Yoshiyasu Ozeki

Publication date: 12 April 2024

Published in: The New York Journal of Mathematics (Search for Journal in Brave)

Abstract: Let $p$ be a prime number and $M$ the extension field of a $p$-adic field $K$ obtained by adjoining all $p$-power roots of all elements of $K$. In this paper, we show that there exists a constant $C$, depending only on $K$ and an integer $g>0$, which satisfies the following property:If $A_{/K}$ is a $g$-dimensional CM abelian variety, then the order of the torsion subgroup of $A(M)$ is bounded by $C$.

Full work available at URL: https://arxiv.org/abs/2209.01811

zbMATH Keywords

abelian varietiescomplex multiplication\(p\)-adic Hodge theory

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Complex multiplication and abelian varieties (14K22)

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