  Let J be the Jacobian of a smooth curve C of genus g, and let A(J) be the
ring of algebraic cycles modulo algebraic equivalence on J, tensored with Q. We
study in this paper the smallest Q-vector subspace R of A(J) which contains C
and is stable under the natural operations of A(J) : intersection and
Pontryagin products, pull back and push down under multiplication by integers.
We prove that this "tautological subring" is generated (over Q) by the classes
of the subvarieties W_1=C, W_2=C+C, ..., W_{g-1}. If C admits a morphism of
degree d onto P^1, we prove that the last d-1 classes suffice.
