Abstract: We investigate the Galois group G_{S}(p) of the maximal p-extension unramified outside a finite set S of primes of a number field in the (mixed) case, when there are primes dividing p inside and outside S. We show that the cohomology of G_{S}(p) is 'often' isomorphic to the étale cohomology of the scheme Spec(O_{k} \ S), in particular, G_{S}(p) is of cohomological dimension 2 then. We deduce this from the results in our previous paper, which mainly dealt with the tame case. |
pdf-file schmidt-bessatsu.pdf.