The de Rham Witt complex, cohomological kernels and p-extensions in characteristic p (original) (raw)

The first two cohomology groups of some Galois groups

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

Field theory and the cohomology of some Galois groups

Arxiv preprint math/0009011, 2000

Abstract. We prove that two arithmetically significant extensions of a field F coincide if and only if the Witt ring WF is a group ring Z/n[G]. Furthermore, working modulo squares with Galois groups which are 2-groups, we establish a theorem analogous to Hilbert's theorem 90 and show ...