MILD PRO-p-GROUPS AS GALOIS GROUPS OVER GLOBAL FIELDS

摘要

This paper is devoted to finding new examples of mild pro-p-groups as Galois groups over global fields, following the work of Labute ([6]). We focus on the Galois group G_S~T of the maximal T-split S-ramified pro-p-extension of a global field k. We first retrieve some facts on presentations of such a group, including a study of the local-global principle for the cohomology group H~2(G_S~T, F_p), then we show separately in the case of function fields and in the case of number fields how it can be used to find some mild pro-p-groups.