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

Published online by Cambridge University Press:  11 January 2016

Yuichiro Hoshi
Yuichiro Hoshi*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japanyuichiro@kurims.kyoto-u.ac.jp
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Abstract

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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.

Keywords

14H3014H10
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 203 , September 2011 , pp. 47 - 100
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2011

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