Non-existence of certain CM abelian varieties with prime power torsion

TL;DR

This paper investigates a conjecture about the finiteness of certain CM abelian varieties with restricted prime power torsion, providing new insights into their existence and classification.

Contribution

It proves the non-existence of certain CM abelian varieties with specified prime power torsion, advancing understanding of their finiteness properties.

Findings

Proves non-existence of specific CM abelian varieties with prime power torsion

Supports Rasmussen and Tamagawa's conjecture on finiteness

Enhances classification of CM abelian varieties with torsion constraints

Abstract

In this paper, we study a conjecture of Rasmussen and Tamagawa, on the finiteness of the set of isomorphism classes of abelian varieties with constrained prime power torsion. Our result is related with abelian varieties which have complex multiplication over their fields of definition.