Factorisability and wildly ramified Galois extensions

Burns, David J.

Annales de l'Institut Fourier, Tome 41 (1991), p. 393-430 / Harvested from Numdam

Résumé

Soit $L/K$ une extension abélienne de corps $p$-adiques, et soit ${\cal O}$ l’anneau de valuation de $K$. Nous étudions les idéaux de l’anneau de valuation de $L$ comme représentations entières du groupe de Galois ${\rm Gal}(L/K)$. À supposer que $K$ soit absolument non ramifiée nous utilisons les techniques de la théorie de la factorisabilité pour examiner quels idéaux sont isomorphes à un ${\cal O}$-ordre dans l’algèbre du groupe $K[{\rm Gal}(l/K)]$. Nous obtenons de nouveaux résultats généraux et aussi explicites.

Abstract

Let $L/K$ be an abelian extension of $p$-adic fields, and let ${\cal O}$ denote the valuation ring of $K$. We study ideals of the valuation ring of $L$ as integral representations of the Galois group ${\rm Gal}(L/K)$. Assuming $K$ is absolutely unramified we use techniques from the theory of factorisability to investigate which ideals are isomorphic to an ${\cal O}$-order in the group algebra $K[{\rm Gal}(l/K)]$. We obtain several general and also explicit new results.

Détail

Publié le : 1991-01-01

MR 92m:11135 | Zbl 0727.11048

DOI : https://doi.org/10.5802/aif.1259

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