An effective Arakelov-theoretic version of the hyperbolic isogeny theorem

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.

References in corpus (2)

• Polynomial bounds for Arakelov invariants of Belyi curves
• Self-intersection of the relative dualizing sheaf on modular curves $X_1(N)$