On parametric extensions over number fields

• François Legrand ^[1]
  1. [1] Tel Aviv University

     Tel Aviv University

     Israel

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 18, Nº 2, 2018, págs. 551-563
• Idioma: inglés
• Enlaces
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• Resumen

  • Given a number field F, a finite group G and an indeterminate T , a G-parametric extension over F is a finite Galois extension E/F(T ) with Galois group G and E/F regular that has all the Galois extensions of F with Galois group G among its specializations. We are mainly interested in producing nonG-parametric extensions, which relates to classical questions in inverse Galois theory like the Beckmann-Black problem. Building on a strategy developed in previous papers, we show that there exists at least one non-G-parametric extension over F for a given non-trivial finite group G and a given number field F under the sole necessary condition that G occurs as the Galois group of a Galois extension E/F(T ) with E/F regular.