Abelian absolute Galois groups

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal Pub Date : 2024-02-02 DOI:10.1017/s0017089524000028

Moshe Jarden

引用次数: 0

Abstract

Generalizing a result of Wulf-Dieter Geyer in his thesis, we prove that if

$K$

is a finitely generated extension of transcendence degree

$r$

of a global field and

$A$

is a closed abelian subgroup of

$\textrm{Gal}(K)$

, then

${\mathrm{rank}}(A)\le r+1$

. Moreover, if

$\mathrm{char}(K)=0$

, then

${\hat{\mathbb{Z}}}^{r+1}$

is isomorphic to a closed subgroup of

$\textrm{Gal}(K)$

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阿贝尔绝对伽罗瓦群

在推广沃尔夫-迪特尔-盖耶尔（Wulf-Dieter Geyer）论文中的一个结果的基础上，我们证明，如果 $K$ 是一个全域的超越度 $r$ 的有限生成扩展，并且 $A$ 是 $\textrm{Gal}(K)$ 的一个封闭无边子群，那么 ${mathrm{rank}}(A)\le r+1$ 。此外，如果 $\mathrm{char}(K)=0$ ，那么 ${hat\mathbb{Z}}^{r+1}$ 与 $textrm{Gal}(K)$ 的一个封闭子群同构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Glasgow Mathematical Journal 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Glasgow Mathematical Journal publishes original research papers in any branch of pure and applied mathematics. An international journal, its policy is to feature a wide variety of research areas, which in recent issues have included ring theory, group theory, functional analysis, combinatorics, differential equations, differential geometry, number theory, algebraic topology, and the application of such methods in applied mathematics. The journal has a web-based submission system for articles. For details of how to to upload your paper see GMJ - Online Submission Guidelines or go directly to the submission site.