On the Structure of the Weil Restriction of Abelian Varieties

TL;DR

This paper explores the structure of Weil restrictions of abelian varieties, focusing on their endomorphism rings and how these influence their isogeny decompositions, providing new insights into their algebraic properties.

Contribution

It offers a detailed description of endomorphism rings of Weil restrictions and applies these findings to analyze their isogeny decompositions, advancing understanding in this area.

Findings

Endomorphism rings of Weil restrictions are characterized.

Isogeny decompositions of Weil restrictions are analyzed.

Results enhance understanding of the algebraic structure of Weil restrictions.

Abstract

We give a description of endomorphism rings of Weil restrictions of abelian varieties with respect to finite Galois extensions. The results are applied to study the isogeny decomposition of Weil restrictions.