October 2024 On a geometric version of the Grothendieck conjecture for configuration spaces of hyperbolic curves
Yu IIJIMA
Author Affiliations +
Hokkaido Math. J. 53(3): 531-548 (October 2024). DOI: 10.14492/hokmj/2023-724

Abstract

Under the C-admissible condition, Hoshi and Mochizuki proved a geometric version of the Grothendieck conjecture for the geometric outer monodromy representation associated to the configuration space of a hyperbolic curve. In the present paper, under conditions concerning the number of cusps of the hyperbolic curve and the dimension of the configuration space, we remove the C-admissible condition from the result of Hoshi and Mochizuki.

Acknowledgment

The author would like to thank Yuichiro Hoshi for explaining to him the arguments used in the proof of Theorem 3.4. The author was supported by JSPS KAKENHI Grant Number 20K14290.

Citation

Download Citation

Yu IIJIMA. "On a geometric version of the Grothendieck conjecture for configuration spaces of hyperbolic curves." Hokkaido Math. J. 53 (3) 531 - 548, October 2024. https://doi.org/10.14492/hokmj/2023-724

Information

Received: 18 April 2023; Revised: 31 July 2023; Published: October 2024
First available in Project Euclid: 17 October 2024

Digital Object Identifier: 10.14492/hokmj/2023-724

Subjects:
Primary: 14H30
Secondary: 14H10

Keywords: combinatorial anabelian geometry , configuration space of a hyperbolic curve , geometric version of the Grothendieck conjecture

Rights: Copyright c 2024 Hokkaido University, Department of Mathematics

Vol.53 • No. 3 • October 2024
Back to Top