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Cohomological dimension and Schreier's formula in Galois cohomology

Research paper by John Labute, Nicole Lemire, Jan Minac, John Swallow

Indexed on: 02 Mar '05Published on: 02 Mar '05Published in: Mathematics - Number Theory



Abstract

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).