2016/02/22 by Legrand, François
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1602.06706
Given a number field F, a finite group G and an indeterminate T, \ita 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 non-G-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.