On arithmetic inequalities for points of bounded degree

TL;DR

This paper explores how a conjecture by Schlickewei could lead to new inequalities in the distribution of algebraic points of bounded degree on polarized projective varieties, refining existing methods.

Contribution

It introduces a refined filtration and Subspace Theorem approach to study integral points, connecting conjectural assumptions to new arithmetic inequalities.

Findings

Conditional inequalities for algebraic points of bounded degree

Refined filtration construction improves analysis of integral points

Links Schlickewei's conjecture to Second Main Arithmetic Schmidt inequalities

Abstract

We study algebraic points of bounded degree on polarized projective varieties. To do so, we refine further the filtration construction and Subspace Theorem approach, for the study of integral points, which has origins in the work of Corvaja-Zannier, Levin, Evertse and Autissier. Our main result shows how a conjecture of H.~P.~Schlickewei implies Second Main Arithmetic Schmidt's Subspace type inequalities for polarized projective varieties and points of bounded degree.