2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77350In this paper, we propose a new height function for a variety defined over a finitely generated field over Q. For this height function, we will prove Northcott's theorem and Bogomolov's conjecture, so that we can recover the original Raynaud's theorem (Manin-Mumford's conjecture).35 or 36 pages, re-write several partsNumber TheoryAlgebraic Geometry11G35;14G25;14G40;11G10;14K15text