Rings of integers of type $K(π,1)$

Details Rings of integers of type $K(π,1)$ Rings of integers of type $K(π,1)$

2007-05-23

arxiv.org/abs/0705.3372v2

Mathematics

Number Theory

final version, to appear in documenta mathematica

Scientific paper

We investigate the Galois group $G_S(p)$ of the maximal $p$-extension
unramified 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 $\Spec(\O_k \sm
S)$, in particular, $G_S(p)$ is of cohomological dimension~2 then.

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