Non-existence and splitting theorems for normal integral bases

2008/01/15 by Cornélius Greither, Cornelius Greither, Greither, Cornelius +2
Computer Science · Mathematics · #11R18 #11R33 #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT #msc:11R18 #msc:11R33

paper · pdf · doi:10.48550/arxiv.0801.2272

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

openalex publication_date 2008/01/15 · arxiv created 2009/02/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 ⊂ K ⊂ L forces the tower to be split in a very strong sense.

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