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An effective Arakelov-theoretic version of the hyperbolic isogeny theorem

Published online by Cambridge University Press:  14 January 2016

Institut für Mathematik, Johannes Gutenberg-Universität, Mainz, Germany. e-mail:


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.

Research Article
Copyright © Cambridge Philosophical Society 2016 

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