  For an abelian number field K containing a primitive p-th root of unity (p an
odd prime) and satisfying certain technical conditions, we parametrize the
Z_p[G(K/Q)]-annihilators of the "minus" part A_K^- of the p-class group by
means of modules of Jacobi sums. Using a reflection theorem and Bloch-Kato's
reciprocity law, we then determine the Fitting ideal of the "plus" part A_K^+
in terms of "twisted" Gauss sums.
