grothendieck - teichm ller群的组合Belyi Cuspidalization和算术子商

IF 1.1 2区数学 Q1 MATHEMATICS

Publications of the Research Institute for Mathematical Sciences Pub Date : 2020-10-07 DOI:10.4171/prims/56-4-5

Shota Tsujimura

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引用次数: 8

摘要

在本文中，我们对Mochizuki提出的Belyi尖化理论进行了某种组合版本的发展。为代数数∈C的子域写Q⊆C。然后，我们将组合Belyi尖化理论应用于Grothendieck-Teichmüller群的某些自然闭子群，这些子群与p-adic数[其中p是素数]的域相关联，并应用于Q的稳定的×μ-不可分子域，即。，每个有限域扩展都满足域扩展中的每个非零可整除元素是单位根的性质的子域。2010年数学学科分类：小学14H30。

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Combinatorial Belyi Cuspidalization and Arithmetic Subquotients of the Grothendieck–Teichmüller Group

In this paper, we develop a certain combinatorial version of the theory of Belyi cuspidalization developed by Mochizuki. Write Q ⊆ C for the subfield of algebraic numbers ∈ C. We then apply this theory of combinatorial Belyi cuspidalization to certain natural closed subgroups of the Grothendieck-Teichmüller group associated to the field of p-adic numbers [where p is a prime number] and to stably ×μ-indivisible subfields of Q, i.e., subfields for which every finite field extension satisfies the property that every nonzero divisible element in the field extension is a root of unity. 2010 Mathematics Subject Classification: Primary 14H30.

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来源期刊

Publications of the Research Institute for Mathematical Sciences 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The aim of the Publications of the Research Institute for Mathematical Sciences (PRIMS) is to publish original research papers in the mathematical sciences.