%0 Journal Article
%T Cohomological dimension and Schreier's formula in Galois cohomology
%A John Labute
%A Nicole Lemire
%A Jan Minac
%A John Swallow
%J Mathematics
%D 2004
%I arXiv
%X Let p be a prime and F a field containing a primitive pth root of unity. Then for n in N, the cohomological dimension of the maximal pro-p-quotient G of the absolute Galois group of F is <=n if and only if the corestriction maps H^n(H,Fp) -> H^n(G,Fp) are surjective for all open subgroups H of index p. Using this result we derive a surprising generalization to dim_Fp H^n(H,Fp) of Schreier's formula for dim_Fp H^1(H,Fp).
%U http://arxiv.org/abs/math/0411446v2