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

Alexander Schmidt

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

Number Theory 2007-11-14 v2

Authors: Alexander Schmidt

Abstract

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.

Keywords

rings of integers galois groups p-extensions etale cohomology cohomological dimension number fields k(pi,1)

Cite

@article{arxiv.0705.3372,
  title  = {Rings of integers of type $K(\pi,1)$},
  author = {Alexander Schmidt},
  journal= {arXiv preprint arXiv:0705.3372},
  year   = {2007}
}

Comments

final version, to appear in documenta mathematica

Related papers

View all related →