Nagoya Mathematical Journal

Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero

Yuichiro Hoshi

Abstract

Let $l$ be a prime number. In this paper, we prove that the isomorphism class of an $l$-monodromically full hyperbolic curve of genus zero over a finitely generated extension of the field of rational numbers is completely determined by the kernel of the natural pro-$l$ outer Galois representation associated to the hyperbolic curve. This result can be regarded as a genus zero analogue of a result due to Mochizuki which asserts that the isomorphism class of an elliptic curve which does not admit complex multiplication over a number field is completely determined by the kernels of the natural Galois representations on the various finite quotients of its Tate module.

Article information

Source
Nagoya Math. J., Volume 203 (2011), 47-100.

Dates
First available in Project Euclid: 18 August 2011

https://projecteuclid.org/euclid.nmj/1313682312

Digital Object Identifier
doi:10.1215/00277630-1331863

Mathematical Reviews number (MathSciNet)
MR2834249

Zentralblatt MATH identifier
1246.14041

Subjects
Secondary: 14H10: Families, moduli (algebraic)

Citation

Hoshi, Yuichiro. Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero. Nagoya Math. J. 203 (2011), 47--100. doi:10.1215/00277630-1331863. https://projecteuclid.org/euclid.nmj/1313682312

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