The first two cohomology groups of some Galois groups

Details The first two cohomology groups of some Galois groups The first two cohomology groups of some Galois groups

2003-04-15

arxiv.org/abs/math/0304202v1

Mathematics

Number Theory

Scientific paper

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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