Parshin's method and the geometric Bombieri-Lang conjecture

Abstract

In this short survey, we explain Parshin's proof of the geometric Bombieri-Lang conjecture, and show that it can be used to give an alternative proof of Xie-Yuan's recent resolution of the geometric Bombieri-Lang conjecture for projective varieties with empty special locus and admitting a finite morphism to a traceless abelian variety.

arXiv comment10 pages. Survey note. Jacob Murre SI v2. minor improvements