Combinatorial Belyi cuspidalization and arithmetic subquotients of the Grothendieck-Teichmüller group. (English) Zbl 1460.14068
Summary: In this paper, we develop a certain combinatorial version of the theory of Belyi cuspidalization developed by Mochizuki. Write \({\overline{\mathbb{Q}}} \subseteq \mathbb{C}\) for the subfield of algebraic numbers \(\in \mathbb{C} \). 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 \(\times \mu\)-indivisible subfields of \({\overline{\mathbb{Q}}} \), 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.
MSC:
| 14H30 | Coverings of curves, fundamental group |
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