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An effective Arakelov-theoretic version of the hyperbolic isogeny theorem

Published online by Cambridge University Press:  14 January 2016

ARIYAN JAVANPEYKAR
ARIYAN JAVANPEYKAR*
Affiliation:
Institut für Mathematik, Johannes Gutenberg-Universität, Mainz, Germany. e-mail: ariyanjavan@gmail.com
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Abstract

For any integer e and hyperbolic curve X over $\overline{\mathbb Q}$, Mochizuki showed that there are only finitely many isomorphism classes of hyperbolic curves Y of Euler characteristic e with the same universal cover as X. We use Arakelov theory to prove an effective version of this finiteness statement.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 160 , Issue 3 , May 2016 , pp. 463 - 476
Copyright
Copyright © Cambridge Philosophical Society 2016 

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References

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