Geodesic
Rings of integers of type $K(\pi,1)$
Documenta mathematica, Tome 12 (2007), pp. 441-471
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We investigate the Galois group GS​(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 GS​(p) is 'often' isomorphic to the étale cohomology of the scheme Spec(Ok​∖S), in particular, GS​(p) is of cohomological dimension 2 then.
DOI : 10.4171/dm/230
Classification : 11R34, 12G10
Mots-clés : cohomological dimension, Galois cohomology, restricted ramification 
@article{10_4171_dm_230,
     author = {Alexander Schmidt},
     title = {Rings of integers of type $K(\pi,1)$},
     journal = {Documenta mathematica},
     pages = {441--471},
     year = {2007},
     volume = {12},
     doi = {10.4171/dm/230},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/230/}
}
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%D 2007
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Alexander Schmidt. Rings of integers of type $K(\pi,1)$. Documenta mathematica, Tome 12 (2007), pp. 441-471. doi: 10.4171/dm/230

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