## Kodai Mathematical Journal

### The Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one

#### 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.

#### Article information

Source
Kodai Math. J., Volume 40, Number 3 (2017), 625-637.

Dates
Revised: 20 February 2017
First available in Project Euclid: 31 October 2017

https://projecteuclid.org/euclid.kmj/1509415237

Digital Object Identifier
doi:10.2996/kmj/1509415237

Mathematical Reviews number (MathSciNet)
MR3718502

Zentralblatt MATH identifier
06827108

#### Citation

Hoshi, Yuichiro; Kinoshita, Ryo; Nakayama, Chikara. The Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one. Kodai Math. J. 40 (2017), no. 3, 625--637. doi:10.2996/kmj/1509415237. https://projecteuclid.org/euclid.kmj/1509415237