no. 1
Non-existence and splitting theorems for normal integral bases
[Théorèmes de non-existence et de décomposition pour les bases normales entières]
Greither, Cornelius1 ; Johnston, Henri2
1 Universität der Bundeswehr München Fakultät für Informatik Institut für theoretische Informatik und Mathematik 85577 Neubiberg (Germany)
2 St. John’s College Cambridge CB2 1TP (United Kingdom)
Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 417-437.

Nous établissons de nouvelles conditions sous lesquelles il ne peut exister de bases normales entières (faibles) dans les extensions galoisiennes modérées de corps de nombres. Ceci nous conduit au résultat suivant : sous quelques hypothèses techniques convenables, l’existence d’une base normale entière dans l’étage supérieur d’une tour abélienne ℚ⊂K⊂L force que la tour se décompose dans un sens très fort.

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.

DOI : 10.5802/aif.2709
Classification : 11R33, 11R18, 11R20
Keywords: Normal integral basis
Mot clés : base normale entière
Greither, Cornelius 1 ; Johnston, Henri 2

1 Universität der Bundeswehr München Fakultät für Informatik Institut für theoretische Informatik und Mathematik 85577 Neubiberg (Germany)
2 St. John’s College Cambridge CB2 1TP (United Kingdom) 
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Greither, Cornelius; Johnston, Henri. Non-existence and splitting theorems for normal integral bases. Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 417-437. doi : 10.5802/aif.2709. http://www.numdam.org/articles/10.5802/aif.2709/

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