2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139197Using morphic cohomology, we produce a sequence of conjectures, called morphic conjectures, which terminates at the Grothendieck standard conjecture A. A refinement of Hodge structures is given, and with the assumption of morphic conjectures, we prove a Hodge index theorem. We answer a question of Friedlander and Lawson by assuming the Grothendieck standard conjecture B and prove that the topological filtration from morphic cohomology is equal to the Grothendieck arithmetic filtration for some cases.17 pages. Some results are added and simplifiedAlgebraic Geometry14C25; 14C30text