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Décomposition du Galois-module des entiers d'une extension cyclique de degré premier d'un corps de nombres ou d'un corps local

Françoise Bertrandias (1979)

Annales de l'institut Fourier

Soit A un anneau de Dedekind, de corps des fractions K , et soit L une extension galoisienne de K , dont le groupe de Galois G est cyclique d’ordre premier. On note B la clôture intégrale de A dans L . Il existe une unique décomposition du A [ G ] -module B en somme directe de sous-modules indécomposables. On détermine cette décomposition lorsque K est un corps local ou un corps de nombres. Le résultat dépend d’une part des caractères irréductibles de G sur K , d’autre part des nombres de ramification associés...

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