SUR LA PROPAGATION DE LA PROPRIÉTÉ MILD AU-DESSUS D'UNE EXTENSION QUADRATIQUE IMAGINAIRE DE Q

Abstract : In this work, we are interested in the pro-p groups G_S , which are Galois groups of maximal pro-p extensions of number fields unramified outside a finite set S of primes not dividing p. We focus on whether the mildness property is preserved over imaginary quadratic extensions. Our starting point is Labute-Schmidt's criterion ([12]), based on the study of the cup-product on the first cohomology group H_1(G_S , F_p). In favourable conditions, we show by computation that the group we study often satisfies a weak version (LS_f) of Labute-Schmidt's criterion. Then, a theoretical criterion is established for proving mildness of some groups to which the (LS_f) criterion does not apply. This theoretical criterion is finally illustrated by examples for p = 3 and compared to Labute and Vogel's works ([9] et [16]).
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Marine Rougnant. SUR LA PROPAGATION DE LA PROPRIÉTÉ MILD AU-DESSUS D'UNE EXTENSION QUADRATIQUE IMAGINAIRE DE Q. Annales mathématiques du Quebec, 2016, 41 (2), pp.309--335. ⟨10.1007/s40316-016-0071-9⟩. ⟨hal-01390775⟩

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