#### DOCUMENTA MATHEMATICA, Vol. 12 (2007), 441-471

Alexander Schmidt

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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