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

2022/09/05 by Ozeki, Yoshiyasu
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2209.01811

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.

Related

• Torsion of abelian varieties and Lubin-Tate extensions
• Bounds for torsion on abelian varieties with integral moduli
• Torsion bounds for a fixed abelian variety and varying number field
• Torsion of Abelian varieties over solvable extensions of number fields
• Torsion points of abelian varieties with values in infinite extensions over a p-adic field