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arXiv · 1612.06577

Non-parametric sets of regular realizations over number fields

Joachim König·François Legrand
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Abstract

Given a number field $k$, we show that, for many finite groups $G$, all the Galois extensions of $k$ with Galois group $G$ cannot be obtained by specializing any given finitely many Galois extensions $E/k(T)$ with Galois group $G$ and $E/k$ regular. Our examples include abelian groups, dihedral groups, symmetric groups, general linear groups over finite fields, etc. We also provide a similar conclusion while specializing any given infinitely many Galois extensions $E/k(T)$ with Galois group $G$ and $E/k$ regular of a certain type, under a conjectural "uniform Faltings" theorem".

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Joachim König, François Legrand. 2017-10-24. Non-parametric sets of regular realizations over number fields. https://arxiv.org/abs/1612.06577

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