Rings of integers of type $K(\pi,1)$
Copyright policy )Rings of integers of type $K(\pi,1)$
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 \mathit{Spec}({\mathcal O}_k \setminus S) , in particular, G_S(p) is of cohomological dimension 2 then.
11R34, Mathematics - Number Theory, 12G10, Cohomological dimension of fields, restricted ramification, cohomological dimension, maximal \(p\)-extensions, Galois cohomology, FOS: Mathematics, Number Theory (math.NT), 11R34 ; 12G10
11R34, Mathematics - Number Theory, 12G10, Cohomological dimension of fields, restricted ramification, cohomological dimension, maximal \(p\)-extensions, Galois cohomology, FOS: Mathematics, Number Theory (math.NT), 11R34 ; 12G10
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