论文标题
有限组在数字字段上的局部维度
The local dimension of a finite group over a number field
论文作者
论文摘要
令$ g $为有限的组，$ k $一个数字。我们构建了$ g $ - extension $ e/f $，具有$ f $超越学位$ 2 $ $ 2 $上的$ k $，专门针对所有$ g $ - extensions $ k_ \ mathfrak {p} $，其中$ \ mathfrak {p} $在所有$ k $ of $ k $的primes by Bloctal primes by中都运行。如果此外，如果$ g $具有超过$ k $的通用扩展，我们表明扩展名$ e/f $具有所谓的希尔伯特·格伦瓦尔德（Hilbert-Grunwald）物业。将这些结果与$ k $ $ k $的基本维度的概念及其算术类似物进行了比较。
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.
