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

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.