2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155293We prove an absolute Chow-Kuenneth decomposition for the motive of universal families A of abelian varieties over some compact Shimura surface. We furthermore prove the Hodge conjecture for general fibres of A, extending results of Ribet.18 pages, typos and enlarged introductionAlgebraic GeometryNumber Theorytext