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October 2021 Geometric version of the Grothendieck conjecture for universal curves over Hurwitz stacks
Shota Tsujimura
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Kodai Math. J. 44(3): 492-555 (October 2021). DOI: 10.2996/kmj/kmj44305

Abstract

In this paper, we prove a certain geometric version of the Grothendieck Conjecture for tautological curves over Hurwitz stacks. This result generalizes a similar result obtained by Hoshi and Mochizuki in the case of tautological curves over moduli stacks of pointed smooth curves. In the process of studying this version of the Grothendieck Conjecture, we also examine various fundamental geometric properties of "profiled log Hurwitz stacks", i.e., log algebraic stacks that parametrize Hurwitz coverings for which the marked points are equipped with a certain ordering determined by combinatorial data which we refer to as a "profile".

Acknowledgment

The author would like to thank Professor Yuichiro Hoshi and Professor Shinichi Mochizuki for introducing me to the field of combinatorial anabelian geometry and for many helpful discussions, as well as for their warm encouragement. Moreover, the author also would like to thank the referee for reading carefully and giving the author valuable suggestions.

Citation

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Shota Tsujimura. "Geometric version of the Grothendieck conjecture for universal curves over Hurwitz stacks." Kodai Math. J. 44 (3) 492 - 555, October 2021. https://doi.org/10.2996/kmj/kmj44305

Information

Received: 9 May 2018; Revised: 9 June 2021; Published: October 2021
First available in Project Euclid: 27 October 2021

Digital Object Identifier: 10.2996/kmj/kmj44305

Subjects:
Primary: 14H30
Secondary: 14H10

Keywords: Anabelian geometry , Grothendieck conjecture , Hurwitz stack , universal curve

Rights: Copyright © 2021 Tokyo Institute of Technology, Department of Mathematics

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Vol.44 • No. 3 • October 2021
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