On the equivariant structure of ideals in abelian extensions of local fields (with an appendix by W. Bley)

Abstract

Let p be an odd rational prime and K a finite extension of ${\mathbb{Q}}_p$ . We give a complete classification of those finite abelian extensions $L/K$ in which any ideal of the valuation ring of L is free over its associated order in ${\mathbb{Q}}_p[Gal(L/K)]$ . In an appendix W. Bley describes an algorithm which can be used to determine the structure of Galois stable ideals in abelian extensions of number fields. The algorithm is applied to give several new and interesting examples.