2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74734We prove a large sieve statement for the average distribution of Frobenius conjugacy classes in arithmetic monodromy groups over finite fields. As a first application we prove a stronger version of a result of Chavdarov on the ``generic'' irreducibility of the numerator of the zeta functions in a family of curves with large monodromy.30 pagesNumber TheoryAlgebraic Geometry11N35, 11G25, 14G15; 14D10, 11C08text