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We investigate the Galois group $G_S(p)$ of the maximal $p$-extensionunramified outside a finite $S$ of primes of a number field in the (tame) case,when no prime dividing $p$ is in $S$. We show that the cohomology of $G_S(p)$is 'often' isomorphic to the etale cohomology of the scheme $\Spec(\O_k \smS)$, in particular, $G_S(p)$ is of cohomological dimension~2 then.

Rings of integers of type $K(\pi,1)$