A Buium--Coleman bound for the Zilber--Pink conjecture for curves inside abelian varieties

Abstract

We provide an explicit bound for the image of the Zilber--Pink locus of a curve in an abelian variety under reduction modulo a suitably large prime $p$. We also provide a new proof of finiteness of the Zilber--Pink locus. Under further assumptions on the abelian variety, we prove a bound on the size of the locus.