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Nombres de Weil, sommes de Gauss et annulateurs Galoisiens
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 133, Number 6, December 2011
- pp. 1533-1571
- 10.1353/ajm.2011.0042
- Article
- Additional Information
For an abelian number field $K$ containing a primitive $p^{{\rm th}}$ root
of unity ($p$ an odd prime) and satisfying certain technical conditions,
we parametrize the ${\Bbb Z}_p[{\rm G}(K/\Bbb{Q})]$-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.