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- W4301432287 abstract "Given a number field $F$, a finite group $G$ and an indeterminate $T$, {it{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 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." @default.
- W4301432287 created "2022-10-05" @default.
- W4301432287 creator A5074703588 @default.
- W4301432287 date "2016-02-22" @default.
- W4301432287 modified "2023-09-30" @default.
- W4301432287 title "On parametric extensions over number fields" @default.
- W4301432287 doi "https://doi.org/10.48550/arxiv.1602.06706" @default.
- W4301432287 hasPublicationYear "2016" @default.
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