An effective Arakelov-theoretic version of the hyperbolic isogeny theorem

Abstract

AbstractFor any integereand hyperbolic curveXover$\overline{\mathbb Q}$, Mochizuki showed that there are only finitely many isomorphism classes of hyperbolic curvesYof Euler characteristicewith the same universal cover asX. We use Arakelov theory to prove an effective version of this finiteness statement.