
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.
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