2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114236We apply the classical technique on cyclic objects of Alain Connes to various objects, in particular to the higher Chow complex of S. Bloch to prove a Connes periodicity long exact sequence involving motivic cohomology groups. The Cyclic higher Chow groups and the Connes higher Chow groups of a variety are defined in the process and various properties of them are deduced from the known properties of the higher Chow groups. Applications include an equivalent reformulation of the Beilinson-Soulé vanishing conjecture for the motivic cohomology groups of a smooth variety $X$ and a reformulation of the conjecture of Soulé on the order of vanishing of the zeta function of an arithmetic variety.25 pagesAlgebraic GeometryK-Theory and Homology14C25; 19D55text