Quelques résultats effectifs concernant les invariants de Tsfasman-Vlăduţ
Lebacque, Philippe1
1 Laboratoire de mathématiques de Besançon 16 route de Gray 25030 Besançon cedex (France)
Annales de l'Institut Fourier, Tome 65 (2015) no. 1, pp. 63-99.

On considère dans cet article les propriétés asymptotiques de corps globaux à travers l’étude de leurs invariants de Tsfasman-Vlăduţ, nombres qui décrivent en particulier la décomposition des places dans les tours de corps globaux. On utilise des résultats récents d’Alexander Schmidt et une version faible mais effective du théorème de Grunwald-Wang pour construire des corps globaux infinis ayant un ensemble fini donné d’invariants non nuls et un ensemble prescrit d’invariants nuls, tout en estimant leur défaut.

We consider in this article properties of infinite algebraic extensions of global fields through their Tsfasman-Vladuts invariants, which describe in particular the decomposition of primes in global field towers. We use recent results of A. Schmidt and a weak effective version of the Grunwald-Wang theorem to construct infinite global fields having at the same time a given finite set of positive invariants, a prescribed set of invariants being zero, and a controlled deficiency.

DOI : 10.5802/aif.2925
Classification : 11R29, 11R34, 11R37, 11R45, 11R58
Mot clés : Corps globaux infinis, mild pro-$p$-groupes, ramification restreinte, théorie du corps de classes
Keywords: Infinite global fields, mild pro-$p$-groups, restricted ramification, class field theory
Lebacque, Philippe 1

1 Laboratoire de mathématiques de Besançon 16 route de Gray 25030 Besançon cedex (France) 
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Lebacque, Philippe. Quelques résultats effectifs concernant les invariants de Tsfasman-Vlăduţ. Annales de l'Institut Fourier, Tome 65 (2015) no. 1, pp. 63-99. doi : 10.5802/aif.2925. http://www.numdam.org/articles/10.5802/aif.2925/

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