2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64033We study the interplay between canonical heights and endomorphisms of an abelian variety $A$ over a number field $k$. In particular we show that whenever the ring of endomorphisms defined over $k$ is strictly larger than $\Z$ there will be $\Q$-linear relations among the values of a canonical height-pairing evaluated at a basis modulo torsion of $A(k)$.14 pages, exposition improved, to appear in Bulletin of the Canadian Mathematical SocietyAlgebraic GeometryNumber Theory11G10, 14K15text