Cohomological Dimension and Schreier's Formula in Galois Cohomology

Canadian mathematical bulletin

关键词: cohomological dimension;    Schreier's formula;    Galois theory;    $p$-extensions;    pro-$p$-groups;   

DOI  :  10.4153/CMB-2007-056-3

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $p$ be a prime and $F$ a field containing a primitive $p$-throot of unity. Then for $nin N$, the cohomological dimensionof the maximal pro-$p$-quotient $G$ of the absolute Galois groupof $F$ is at most $n$ if and only if the corestriction maps$H^n(H,Fp) o H^n(G,Fp)$ are surjective for all opensubgroups $H$ of index $p$. Using this result, we generalizeSchreier's formula for $dim_{Fp} H^1(H,Fp)$ to $dim_{Fp}H^n(H,Fp)$.

【 授权许可】

Unknown