Kodai Mathematical Journal

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

Yuichiro Hoshi, Ryo Kinoshita, and Chikara Nakayama

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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
Received: 1 December 2016
Revised: 20 February 2017
First available in Project Euclid: 31 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1509415237

Digital Object Identifier
doi:10.2996/kmj/1509415237

Mathematical Reviews number (MathSciNet)
MR3718502

Zentralblatt MATH identifier
06827108

Subjects
Primary: 14H30: Coverings, fundamental group [See also 14E20, 14F35]
Secondary: 20F34: Fundamental groups and their automorphisms [See also 57M05, 57Sxx]

Keywords
anabelian geometry Grothendieck conjecture moduli space hyperbolic curve configuration space

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


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