Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The local dimension of a finite group over a number field   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.

14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th