Canonical Kahler metrics and Arithmetics -- Generalising Faltings heights
arXiv:1508.07716 · doi:10.1215/21562261-2017-0023
Abstract
We extend the Faltings modular heights of abelian varieties to general arithmetic varieties and show direct relations with the Kahler-Einstein geometry, the Minimal Model Program, heights of Bost and Zhang, and give some applications. Along the way, we propose arithmetic Yau-Tian-Donaldson conjecture, an equivalence of a purely arithmetic property of variety and its metrical property, and partially confirm it.
47 pages. Final version, to appear in Kyoto Journal of Mathematics
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