2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76693In this note, we would like to propose a suitable extension of the arithmetic Chow group of codimension one, in which the Hodge index theorem holds. We also prove an arithmetic analogue of Bogomolov's instability theorem for rank 2 vector bundles on arbitrary regular projective arithmetic varieties.Version 2.0 (30 pages), typeseted by AmSLaTeX, Change the title and extend contentsAlgebraic Geometrytext