Finiteness of non-constant maps over a number field

Motivated by the intermediate Lang conjectures on hyperbolicity and rational points, we prove new finiteness results for non-constant morphisms from a fixed variety to a fixed variety defined over a number field by applying Faltings’s finiteness results to moduli spaces of maps.

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Received 19 August 2021

Received revised 22 November 2021

Accepted 21 December 2021

Published 14 May 2024