2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147089In this note, we will give a partial answer for arithmetic analogues of Grothendieck's standard conjectures due to H. Gillet and C. Soule. (Remark : I changed the title of this note.)9 pages, AmSTeXAlgebraic GeometryHodge index theorem for arithmetic cycles of codimension onetext