On the uniform Rasmussen-Tamagawa conjecture in the CM case

TL;DR

This paper proves a uniform finiteness conjecture for CM abelian varieties, extending previous results from CM elliptic curves to higher-dimensional cases, thereby advancing understanding in arithmetic geometry.

Contribution

It establishes a uniform version of the Rasmussen-Tamagawa conjecture for CM abelian varieties of any dimension, broadening the scope from elliptic curves.

Findings

Proves a uniform finiteness result for CM abelian varieties.

Extends results from CM elliptic curves to higher dimensions.

Contributes to the understanding of the arithmetic of CM abelian varieties.

Abstract

We prove a uniform version of a finiteness conjecture due to Rasmussen and Tamagawa in the case of CM abelian varieties. This extends recent results concerning CM elliptic curves to CM abelian varieties of arbitrary dimension.