English

The first two cohomology groups of some Galois groups

Number Theory 2007-05-23 v1

Abstract

We investigate the first two Galois cohomology groups of pp-extensions over a base field which does not necessarily contain a primitive ppth root of unity. We use twisted coefficients in a systematic way. We describe field extensions which are classified by certain residue classes modulo pnp^nth 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 pp is outlined.

Keywords

Cite

@article{arxiv.math/0304202,
  title  = {The first two cohomology groups of some Galois groups},
  author = {Jan Minac and Adrian Wadsworth},
  journal= {arXiv preprint arXiv:math/0304202},
  year   = {2007}
}