  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).
