On the Schmidt Subspace Theorem

TL;DR

This paper extends the Schmidt Subspace Theorem to algebraic points of bounded degree, providing new results for quadratic points and resolving a conjecture, thereby advancing Diophantine approximation theory.

Contribution

It introduces generalized versions of the Schmidt Subspace Theorem applicable to algebraic points of bounded degree, including quadratic points, and proves a conjecture of Schlickewei.

Findings

Sharp version of Schmidt's theorem for quadratic points in the projective plane

Resolution of Schlickewei's conjecture for algebraic points of bounded degree

Generalized results applicable to various settings in Diophantine approximation

Abstract

We study extensions and generalizations of the Schmidt Subspace Theorem in various settings. In particular, we prove results for algebraic points of bounded degree, giving a sharp version of Schmidt's theorem for quadratic points in the projective plane and a more general result that resolves a conjecture of Schlickewei.