 

Alan Koch
Scaffolds and integral Hopf Galois module structure on purely inseparable extensions view print


Published: 
February 17, 2015

Keywords: 
Hopf Galois extensions, integral Galois module theory, scaffolds 
Subject: 
Primary 16T05. Secondary 11R33, 11S15, 12F15 


Abstract
Let p be prime. Let L/K be a finite, totally ramified, purely inseparable
extension of local fields, [L:K]=p^{n}, 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.


Author information
Department of Mathematics, Agnes Scott College, 141 E. College Ave., Decatur, GA 30030, USA
akoch@agnesscott.edu

