Galois module structure of some elementary p-abelian extensions

2022/03/04 by Lauren R. Heller, Ján Mináč, Heller, Lauren +7
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.2203.02604

Abstract

We determine the Galois module structure of the parameterizing space of elementary p-abelian extensions of a field K when Gal(K/F) is any finite p-group, under the assumption that the maximal pro-p quotient of the absolute Galois group of F is a free, finitely generated pro-p group, and that F contains a primitive pth root of unity if char(F) ≠ p.

Related

• Galois module structure of p^th power classes of abelian extensions of local fields
• Galois Module Structure of pth-Power Classes of Extensions of Degree p
• Relations in the maximal pro-p quotients of absolute Galois groups
• Integral Galois Module Structure for Elementary Abelian Extensions with a Galois Scaffold
• Little galoisian modules