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September 2011 Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero
Yuichiro Hoshi
Nagoya Math. J. 203: 47-100 (September 2011). DOI: 10.1215/00277630-1331863

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.

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

Information

Published: September 2011
First available in Project Euclid: 18 August 2011

zbMATH: 1246.14041
MathSciNet: MR2834249
Digital Object Identifier: 10.1215/00277630-1331863

Subjects:
Primary: 14H30
Secondary: 14H10

Rights: Copyright © 2011 Editorial Board, Nagoya Mathematical Journal

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Vol.203 • September 2011
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