Non-existence and splitting theorems for normal integral bases

Details Non-existence and splitting theorems for normal integral bases Non-existence and splitting theorems for normal integral bases

2008-01-15

arxiv.org/abs/0801.2272v2

Mathematics

Number Theory

17 pages, 4 figures, uses xypic, minor revisions following referee's report. To appear in Annales de L'Institut Fourier

Scientific paper

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.

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