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

  • Alexander Schmidt

Rings of integers of type $K(\pi,1)$ cover
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We investigate the Galois group GS(p)G_S(p) of the maximal pp-extension unramified outside a finite set SS of primes of a number field in the (tame) case, when no prime dividing pp is in SS. We show that the cohomology of GS(p)G_S(p) is 'often' isomorphic to the étale cohomology of the scheme \Spec(\Ok\smS)\Spec({\O}_k \sm S), in particular, GS(p)G_S(p) is of cohomological dimension 2 then.

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Alexander Schmidt, Rings of integers of type K(π,1)K(\pi,1). Doc. Math. 12 (2007), pp. 441–471

DOI 10.4171/DM/230