Intersections of translated algebraic subtori

TL;DR

This paper investigates the intersection properties of translated algebraic subtori within abelian complex algebraic groups, emphasizing torsion translated subtori in algebraic tori, by leveraging classical group correspondence.

Contribution

It introduces a novel approach to intersection theory of translated subgroups using the correspondence between finitely generated abelian groups and abelian complex algebraic reductive groups.

Findings

Characterization of intersection behavior of translated subtori

Results on intersections involving torsion points in algebraic tori

New insights into the structure of translated algebraic subgroups

Abstract

We exploit the classical correspondence between finitely generated abelian groups and abelian complex algebraic reductive groups to study the intersection theory of translated subgroups in an abelian complex algebraic reductive group, with special emphasis on intersections of (torsion) translated subtori in an algebraic torus.