New York Journal of Mathematics
Volume 30 (2024), 422-435


Yoshiyasu Ozeki

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

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Published: March 8, 2024.
Keywords: abelian varieties, complex multiplication, p-adic Hodge theory.
Subject [2010]: 11G10, 14K22.

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.


This work is supported by JSPS KAKENHI Grant Number JP19K03433.

Author information

Yoshiyasu Ozeki
Faculty of Science
Kanagawa University
3-27-1 Rokkakubashi, Kanagawa-ku
Yokohama-shi, Kanagawa 221-8686, JAPAN