Nombres de Weil, sommes de Gauss et annulateurs Galoisiens

Thong Nguyen Quang Do, Vésale Nicolas
2011 American Journal of Mathematics  
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.
doi:10.1353/ajm.2011.0042 fatcat:fvhwqnbpyvfsziewui3qqqz3di