Relative Galois module structure of rings of integers of absolutely Abelian number fields

Details Relative Galois module structure of rings of integers of absolutely Abelian number fields Relative Galois module structure of rings of integers of absolutely Abelian number fields

2006-02-27

arxiv.org/abs/math/0602637v3

Mathematics

Number Theory

18 pages, uses xypic. Completely rewritten following referee's report (note that first version contained serious error). To ap

Scientific paper

Let L/K be an extension of number fields where L/\Q is abelian. We define such an extension to be Leopoldt if the ring of integers O_L of L is free over the associated order A_L/K. Furthermore we define an abelian number field K to be Leopoldt if every finite extension L/K with L/Q abelian is Leopoldt in the sense above. Previous results of Leopoldt, Chan & Lim, Bley, and Byott & Lettl culminate in the proof that the n-th cyclotomic field Q^(n) is Leopoldt for every n. In this paper, we generalize this result by giving more examples of Leopoldt extensions and fields, along with explicit generators.

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