Cohomological dimension and Schreier's formula in Galois cohomology

Details Cohomological dimension and Schreier's formula in Galois cohomology Cohomological dimension and Schreier's formula in Galois cohomology

2004-11-19

arxiv.org/abs/math/0411446v2

Canad. Math. Bull. 50 (2007), no. 4, 588--593

Mathematics

Number Theory

7 pages; removed hypothesis on perfect fields, strengthened main theorem

Scientific paper

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).

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