On the K(π,1)-property for rings of integers in the mixed case

2008/01/14 by Schmidt, Alexander
#11R34 #12G10 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0801.2103

Abstract

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 (mixed) case, when there are primes dividing p inside and outside S. We show that the cohomology of G_S(p) is "often" isomorphic to the etale cohomology of the scheme Spec(O_k S), in particular, G_S(p) is of cohomological dimension 2 then. We deduce this from the results in our previous paper "Rings of integers of type K(π,1)" (arXiv:0705.3372), which mainly dealt with the tame case.

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