The first two cohomology groups of some Galois groups

2003/04/15 by Ján Mináč, Jan Minac, Adrian R. Wadsworth +3
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0304202

arxiv created 2003/04/15 · openalex publication_date 2003/04/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the first two Galois cohomology groups of p-extensions over a base field which does not necessarily contain a primitive pth root of unity. We use twisted coefficients in a systematic way. We describe field extensions which are classified by certain residue classes modulo pⁿth 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.

Related

• Galois Module Structure of pth-Power Classes of Extensions of Degree p
• Quotients of absolute Galois groups which determine the entire Galois cohomology
• Relations in the maximal pro-p quotients of absolute Galois groups
• Galois groups and cohomological functors
• The Bloch--Kato conjecture, decomposing fields, and generating cohomology in degree one