2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66357Assuming the Hodge conjecture for abelian varieties of CM-type, one obtains a good category of abelian motives over the algebraic closure of a finite field and a reduction functor to it from the category of CM-motives. Consequentely, one obtains a morphism of gerbes of fibre functors with certain properties. We prove unconditionally that there exists a morphism of gerbes with these properties, and we classify them.Algebraic GeometryNumber Theory14K99; 11G99; 18D30text