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The first two cohomology groups of some Galois groups

Jan Minac·Adrian Wadsworth
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Abstract

We investigate the first two Galois cohomology groups of $p$-extensions over a base field which does not necessarily contain a primitive $p$th root of unity. We use twisted coefficients in a systematic way. We describe field extensions which are classified by certain residue classes modulo $p^n$th powers of a related field, and we obtain transparent proofs and slight generalizations of some classical results of Albert. The potential application to the cyclicity question for division algebras of degree $p$ is outlined.

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Jan Minac, Adrian Wadsworth. 2003-04-15. The first two cohomology groups of some Galois groups. https://arxiv.org/abs/math/0304202

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