Chow's theorem for semi-abelian varieties and bounds for splitting fields of algebraic tori

TL;DR

This paper generalizes Chow's theorem to semi-abelian varieties, providing new bounds for the degrees of splitting fields of algebraic tori, and enhances understanding of their behavior under field extensions.

Contribution

It extends Chow's theorem from abelian to semi-abelian varieties and establishes optimal bounds for splitting field degrees of algebraic tori.

Findings

Generalization of Chow's theorem to semi-abelian varieties

Proof that algebraic tori split over finite separable extensions

Optimal bounds for degrees of splitting fields

Abstract

A theorem of Chow concerns homomorphisms of two abelian varieties under a primary field extension base change. In this paper we generalize Chow's theorem to semi-abelian varieties. This contributes to different proofs of a well-known result that every algebraic torus splits over a finite separable field extension. We also obtain the best bound for the degrees of splitting fields of tori.