Galois groups of tamely ramified $p$-extensions

Boston, Nigel

Journal de théorie des nombres de Bordeaux, Volume 19 (2007) no. 1, pp. 59-70.

Very little is known regarding the Galois group of the maximal $p$-extension unramified outside a finite set of primes $S$ of a number field in the case that the primes above $p$ are not in $S$. We describe methods to compute this group when it is finite and conjectural properties of it when it is infinite.

On connait très peu à propos du groupe de Galois de la $p$-extension maximale non-ramifiée en dehors d’un ensemble fini $S$ de nombres premiers d’un corps de nombres lorsque les nombres premiers au-dessus de $p$ ne sont pas dans $S$. Nous décrivons des méthodes pour calculer ce groupe quand il est fini et ses propriétées conjecturales quand il est infini.

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