  We 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.
