Cohomological Dimension and Schreier's Formula in Galois Cohomology

• Autores: John Labute, Nicole Lemire, Ján Minác, John Swallow
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 50, Nº 4, 2007, págs. 588-593
• Idioma: inglés
• DOI: 10.4153/cmb-2007-056-3
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• Resumen

  • Let p be a prime and F a field containing a primitive p-th root of unity. Then for n \in {mathbb N}, the cohomological dimension of the maximal pro-p-quotient G of the absolute Galois group of F is at most n if and only if the corestriction maps Hn(H,{mathbb F}p) \to Hn(G,{mathbb F}p) are surjective for all open subgroups H of index p. Using this result, we generalize Schreier's formula for dim{mathbb F}p H1(H,{mathbb F}p) to dim{mathbb F}p Hn(H, {mathbb F}p).