Canonical Nonclassical Hopf-Galois Module Structure of Nonabelian Galois Extensions

2014/06/26 by Truman, Paul J
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1406.6894

Abstract

Let L/K be a finite Galois extension of local or global fields in characteristic 0 or p with nonabelian Galois group G, and let \mathfrak B be a G-stable fractional ideal of L. We show that \mathfrak B is free over its associated order in K[G] if and only if it is free over its associated order in the Hopf algebra giving the canonical nonclassical Hopf-Galois structure on the extension.

Related

• Commuting Hopf-Galois Structures on a Separable Extension
• Commutative Hopf-Galois module structure of tame extensions
• Scaffolds and integral Hopf Galois module structure on purely inseparable extensions
• Galois scaffolds for extraspecial p-extensions in characteristic 0
• Galois scaffolds for cyclic pⁿ-extensions in characteristic p