Canonical Kahler metrics and arithmetics: Generalizing Faltings heights

摘要

We extend the Faltings modular heights of Abelian varieties to general arithmetic varieties, show direct relations with the Kahler-Einstem geometry, the minimal model program, and Bost-Zhang's heights and give some applications Along the way, we propose the "arithmetic Yau-Tian-Donaldson conjecture" (the equivalence of a purely arithmetic property of a variety and its metrical property) and partially confirm it.