Commutative Hopf-Galois module structure of tame extensions

2017/08/21 by Truman, Paul J.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1708.06267

Abstract

We prove three theorems concerning the Hopf-Galois module structure of fractional ideals in a finite tamely ramified extension of p -adic fields or number fields which is H -Galois for a commutative Hopf algebra H . Firstly, we show that if L/K is a tame Galois extension of p -adic fields then each fractional ideal of L is free over its associated order in H . We also show that this conclusion remains valid if L/K is merely almost classically Galois. Finally, we show that if L/K is an abelian extension of number fields then every ambiguous fractional ideal of L is locally free over its associated order in H .

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