On arithmetic inequalities for points of bounded degree

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 Schlickewei implies Second Main Arithmetic Schmidt’s Subspace type inequalities for polarized projective varieties and points of bounded degree.