Abstract
We study the Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one. A consequence of the main results is that the isomorphism class of a certain moduli space of hyperbolic curves of genus one over a sub-$p$-adic field is completely determined by the isomorphism class of the étale fundamental group of the moduli space over the absolute Galois group of the sub-$p$-adic field. We also prove related results in absolute anabelian geometry.
Citation
Yuichiro Hoshi. Ryo Kinoshita. Chikara Nakayama. "The Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one." Kodai Math. J. 40 (3) 625 - 637, October 2017. https://doi.org/10.2996/kmj/1509415237
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