  Nori's Eisenstein cohomology classes and their integral refinements due to
Beilinson, Kings and Levin can be used to obtain simple proofs of the
rationality and integrality properties of special values of abelian
$L$-functions of totally real fields. Here we introduce an adelic refinement of
these constructions. This will be used to establish new divisibility properties
of Stickelberger elements associated to abelian extensions of totally real
fields.
