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

  • Shota Tsujimura

    Kyoto University, Japan
Combinatorial Belyi Cuspidalization and Arithmetic Subquotients of the Grothendieck–Teichmüller Group cover

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Abstract

In this paper, we develop a certain combinatorial version of the theory of Belyi cuspidalization developed by Mochizuki. Write for the subfield of algebraic numbers . We then apply this theory of combinatorial Belyi cuspidalization to certain natural closed subgroups of the Grothendieck–Teichmüller group associated to the field of -adic numbers [where is a prime number] and to stably -indivisible subfields of , 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.

Cite this article

Shota Tsujimura, Combinatorial Belyi Cuspidalization and Arithmetic Subquotients of the Grothendieck–Teichmüller Group. Publ. Res. Inst. Math. Sci. 56 (2020), no. 4, pp. 779–829

DOI 10.4171/PRIMS/56-4-5