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

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2024-05-06 DOI:10.1112/jlms.12912

Naganori Yamaguchi

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引用次数: 0

Abstract

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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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

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。

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

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.