Galois groups of tamely ramified $p$-extensions

Boston, Nigel

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

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.

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.

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