On fields with the Property (B) - Archive ouverte HAL
Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2014

On fields with the Property (B)

Résumé

Let K be a number field and let L/K be an infinite Galois extension with Galois group G. Let us assume that G/Z(G) has finite exponent. We show that L has the Property (B) of Bombieri and Zannier: the absolute and logarithmic Weil height on L^* (outside the set of roots of unity) is bounded from below by an absolute constant. We discuss some feature of Property (B): stability by algebraic extensions, relations with field arithmetic. As a as a side result, we prove that the Galois group over Q of the compositum of all totally real fields is torsion free.

Mots clés

Fichier principal
Vignette du fichier
FieldsB.pdf (315.25 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00649954 , version 1 (09-12-2011)

Identifiants

  • HAL Id : hal-00649954 , version 1

Citer

Francesco Amoroso, Sinnou David, Umberto Zannier. On fields with the Property (B). Proceedings of the American Mathematical Society, 2014, 142 (6), pp.1893-1910. ⟨hal-00649954⟩
199 Consultations
339 Téléchargements

Partager

More