  We introduce new motivic invariants of arbitrary varieties over a perfect
field. These cohomological invariants take values in the category of
one-motives (considered up to isogeny in positive characteristic). The
algebraic definition of these invariants presented here proves a conjecture of
Deligne. Applications include some cases of conjectures of Serre, Katz and
Jannsen on the independence of $\ell$ of parts of the \'etale cohomology of
arbitrary varieties over number fields and finite fields.
