有限生成域上仿射双曲曲线的几何m $m$ -步可解格罗登第克猜想

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-06 DOI:10.1112/jlms.12912

Naganori Yamaguchi

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引用次数: 0

摘要

在本文中，我们提出了一些关于无阿贝尔几何中几何上 m $m$ -步可解的格罗内狄克猜想的新结果。具体地说，我们展示了在素数域上有限生成的仿射双曲曲线的（弱双曲和强双曲）几何上 m $m$ -步可解的格罗登第克猜想。首先，我们展示了有限域上的猜想。接着，我们展示了双曲曲线的小田-玉川良好还原准则的几何 m $m$ 步可解版本。最后，利用这两个结果，我们展示了在素域上有限生成的域上的猜想。

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The geometrically m $m$ -step solvable Grothendieck conjecture for affine hyperbolic curves over finitely generated fields

In this paper, we present some new results on the geometrically $m$ -step solvable Grothendieck conjecture in anabelian geometry. Specifically, we show the (weak bianabelian and strong bianabelian) geometrically $m$ -step solvable Grothendieck conjecture(s) for affine hyperbolic curves over fields finitely generated over the prime field. First of all, we show the conjecture over finite fields. Next, we show the geometrically $m$ -step solvable version of the Oda–Tamagawa good reduction criterion for hyperbolic curves. Finally, by using these two results, we show the conjecture over fields finitely generated over the prime field.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.