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
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
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