2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74682We would like to construct a new Grothendieck topology for arithmetic schemes, whose cohomology groups associated with motivic complexes of sheaves are finitely generated and whose Euler characteristics are related to special values of zeta-functions. In this paper we construct this topology for rings of algebraic integers and show that the cohomology of the constant sheaf Z is related to the behavior of zeta-functions at s = 0.31 pagesNumber TheoryAlgebraic Geometry14F20; 11R42, 14F42text