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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.

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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