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.
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.
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
@article{AIF_2015__65_1_63_0, author = {Lebacque, Philippe}, title = {Quelques r\'esultats effectifs concernant les invariants de {Tsfasman-Vl\u{a}du\c{t}}}, journal = {Annales de l'Institut Fourier}, pages = {63--99}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {65}, number = {1}, year = {2015}, doi = {10.5802/aif.2925}, zbl = {1326.11071}, language = {fr}, url = {http://archive.numdam.org/articles/10.5802/aif.2925/} }
TY - JOUR AU - Lebacque, Philippe TI - Quelques résultats effectifs concernant les invariants de Tsfasman-Vlăduţ JO - Annales de l'Institut Fourier PY - 2015 SP - 63 EP - 99 VL - 65 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2925/ DO - 10.5802/aif.2925 LA - fr ID - AIF_2015__65_1_63_0 ER -
%0 Journal Article %A Lebacque, Philippe %T Quelques résultats effectifs concernant les invariants de Tsfasman-Vlăduţ %J Annales de l'Institut Fourier %D 2015 %P 63-99 %V 65 %N 1 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2925/ %R 10.5802/aif.2925 %G fr %F AIF_2015__65_1_63_0
Lebacque, Philippe. Quelques résultats effectifs concernant les invariants de Tsfasman-Vlăduţ. Annales de l'Institut Fourier, Volume 65 (2015) no. 1, pp. 63-99. doi : 10.5802/aif.2925. http://archive.numdam.org/articles/10.5802/aif.2925/
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