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arXiv · 1511.07032

An effective Arakelov-theoretic version of the hyperbolic isogeny theorem

Ariyan Javanpeykar
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Abstract

For an 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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Ariyan Javanpeykar. 2015-11-22. An effective Arakelov-theoretic version of the hyperbolic isogeny theorem. https://doi.org/10.1017/s0305004115000791

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