2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61105We explain the theory of refined cycle maps associated to arithmetic mixed sheaves. This includes the case of arithmetic mixed Hodge structures, and is closely related to work of Asakura, Beilinson, Bloch, Green, Griffiths, Mueller-Stach, Murre, Voisin and others.AMS-TeX, 24 pages, minor change requested by the refereeAlgebraic Geometry14C30, 32S35text