Abstract

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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1533-1571
Launched on MUSE
2011-12-01
Open Access
No
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