Scaffolds and integral Hopf Galois module structure on purely inseparable extensions

2014/05/29 by Koch, Alan
#11R33 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1405.7608

Abstract

Let p be prime. Let L/K be a finite, totally ramified, purely inseparable extension of local fields, [ L:K] =pⁿ, n≥2. It is known that L/K is Hopf Galois for numerous Hopf algebras H, each of which can act on the extension in numerous ways. For a certain collection of such H we construct "Hopf Galois scaffolds" which allow us to obtain a Hopf analogue to the Normal Basis Theorem for L/K. The existence of a scaffold structure depends on the chosen action of H on L. We apply the theory of scaffolds to describe when the fractional ideals of L are free over their associated orders in H.

Related

• Scaffolds and Generalized Integral Galois Module Structure
• Galois scaffolds and Galois module structure in extensions of characteristic p local fields of degree p²
• Hopf Galois Structures on Primitive Purely Inseparable Extensions
• Galois scaffolds for extraspecial p-extensions in characteristic 0
• Galois scaffolds for cyclic pⁿ-extensions in characteristic p