2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58753We prove that for every field k and every positive integer n, there exists an absolutely simple n-dimensional abelian variety over k. We also prove an asymptotic result for finite fields: For every finite field k and positive integer n, we let S(k,n) denote the fraction of the isogeny classes of n-dimensional abelian varieties over k that consist of absolutely simple ordinary abelian varieties. Then for every n, the quantity S(F_q,n) approaches 1 as q approaches infinity over the prime powers.17 pages, AMS-LaTeXAlgebraic GeometryNumber Theory14G15 (Primary) 11G10, 14K15 (Secondary)text