HEIGHT ESTIMATES FOR DOMINANT ENDOMORPHISMS ON PROJECTIVE VARIETIES

Abstract

If φ is a polarizable endomorphism on a projective variety,then the Weil height machine guarantees that φ satis es Northcott's the-orem. In this paper, we show that Northcott's theorem only holds forpolarizable endomorphisms and generalize this result to arbitrary domi-nant endomorphisms: we introduce the height expansion and contractioncoe cients which provide weak Northcott's theorem for dominant endo-morphisms. We also give some applications of the height expansion andcontraction coe cients.