2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69281We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over Q with good reduction outside primes dividing N. Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer--Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over Q with good reduction outside primes dividing N precisely when N is not in the set {1,2,3,5,6,7,10,13}.24 pages, to appear in Manuscripta MathematicaNumber TheoryAlgebraic Geometry14K15text