2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163627Let 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).7 pages; removed hypothesis on perfect fields, strengthened main theoremNumber TheoryK-Theory and Homology12G05; 12G10text