Bounding the Number of Maximal Torsion Cosets on Subvarieties of Algebraic Tori

TL;DR

This paper establishes bounds on the maximum number of torsion cosets on algebraic subvarieties of algebraic tori, employing model theoretic techniques to advance understanding in this area.

Contribution

It introduces new bounds on torsion cosets on subvarieties of algebraic tori using model theoretic methods, a novel approach in this context.

Findings

Derived bounds on the number of maximal torsion cosets

Applied model theoretic methods to algebraic geometry problems

Enhanced understanding of torsion structures in algebraic tori

Abstract

We obtain bounds on the number of maximal torsion cosets for algebraic subvarieties of n-tori, defined over the rationals, using model theoretic methods.