  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.
