2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74272We consider correspondences on smooth quasiprojective varieties $U$. An algebraic cycle inducing the Künneth projector onto $H^1(U)$ is constructed. Assuming normal crossings at infinity, the existence of relative motivic cohomology is shown to imply the independence of $\ell$ for traces of open correspondences.latex 18 pagesAlgebraic GeometryNumber Theorytext