Speaker: Francois Legrand
(Technion):
Title:
Groups without finite parametric sets over Q

Abstract:
Given a finite group G, we consider in this talk "parametric sets'' (over the field Q of rational numbers), that is, sets S of (regular) Galois extensions of Q(T) with Galois group G whose specializations provide all the Galois extensions of Q with Galois group G. This is related to the Beckmann-Black Problem (that asks whether the strategy of solving the Inverse Galois Problem by specializations is optimal) which can be formulated as follows: does a given finite group G have a parametric set over Q?
We show that many finite groups G do not have a finite parametric set over Q.

This is a joint work with Joachim König.