2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135182We construct a singular homology theory on the category of schemes of finite type over a Dedekind domain and verify several basic properties. For arithmetic schemes we construct a reciprocity isomorphism between the integral singular homology in degree zero and the abelianized modified tame fundamental group.final version, to appear in "Algebra & Number Theory"Number TheoryAlgebraic Geometry19E15, 11R37text