Non-existence and splitting theorems for normal integral bases
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We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal integral basis in the upper layer of an abelian tower Q \subset K \subset L forces the tower to be split in a very strong sense.
17 pages, 4 figures, uses xypic, minor revisions following referee's report. To appear in Annales de L'Institut Fourier
17 pages, 4 figures, uses xypic, minor revisions following referee's report. To appear in Annales de L'Institut Fourier