16 citations · 30 across the 15 of their papers we have counts for
9 papers · 1 filter
Hopf-Galois Structures on Non-Normal Extensions of Degree Related to Sophie Germain Primes
Nigel P. Byott, Isabel Martin-Lyons
We consider Hopf-Galois structures on separable (but not necessarily normal) field extensions of squarefree degree . If is the normal closure of then $G=\mathr…
Sufficient Conditions for Large Galois Scaffolds
Nigel P. Byott, G. Griffith Elder
Let be a finite Galois, totally ramified -extension of complete local fields with perfect residue fields of characteristic . In this paper, we give conditions, valid…
Scaffolds and Generalized Integral Galois Module Structure
Nigel P. Byott, Lindsay N. Childs, G. Griffith Elder
Let be a finite, totally ramified -extension of complete local fields with residue fields of characteristic , and let be a -algebra acting on . We define…
Galois scaffolds and Galois module structure in extensions of characteristic local fields of degree
Nigel P. Byott, G. Griffith Elder
A Galois scaffold, in a Galois extension of local fields with perfect residue fields, is an adaptation of the normal basis to the valuation of the extension field, and thus can be…
Integral Galois Module Structure for Elementary Abelian Extensions with a Galois Scaffold
Nigel P. Byott, G. Griffith Elder
This paper justifies an assertion in (Elder, Proc AMS 137 (2009), no 4, 1193--1203) that Galois scaffolds make the questions of Galois module structure tractable. Let be a perf…
A Valuation Criterion for Normal Basis Generators of Hopf-Galois Extensions in Characteristic p
Nigel P. Byott
Let S/R be a finite extension of discrete valuation rings of characteristic p>0, and suppose that the corresponding extension L/K of fields of fractions is separable and is H-Galoi…