Resumen de Cohomological Dimension and Schreier's Formula in Galois Cohomology

John Labute, Nicole Lemire, Ján Minác, John Swallow

• 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).