Rings of Integers of Type $K(,1)$

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 (tame) case, when no prime dividing $p$ is in $S$. We show that the cohomology of $G_S(p)$ is `often' isomorphic to the étale cohomology of the scheme $\Spec(Ø_k \sm S)$, in particular, $G_S(p)$ is of cohomological dimension $2$ then.

2000 Mathematics Subject Classification: 11R34, 12G10

Keywords and Phrases: Galois cohomology, restricted ramification, cohomological dimension

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