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arXiv · 2007.05383

The local dimension of a finite group over a number field

Joachim König·Danny Neftin
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Abstract

Let $G$ be a finite group and $K$ a number field. We construct a $G$-extension $E/F$, with $F$ of transcendence degree $2$ over $K$, that specializes to all $G$-extensions of $K_\mathfrak{p}$, where $\mathfrak{p}$ runs over all but finitely many primes of $K$. If furthermore $G$ has a generic extension over $K$, we show that the extension $E/F$ has the so-called Hilbert-Grunwald property. These results are compared to the notion of essential dimension of $G$ over $K$, and its arithmetic analogue.

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Joachim König, Danny Neftin. 2020-07-10. The local dimension of a finite group over a number field. https://arxiv.org/abs/2007.05383

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