## Kyoto Journal of Mathematics

### Canonical Kähler metrics and arithmetics: Generalizing Faltings heights

Yuji Odaka

#### Abstract

We extend the Faltings modular heights of Abelian varieties to general arithmetic varieties, show direct relations with the Kähler–Einstein 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.

#### Article information

Source
Kyoto J. Math., Volume 58, Number 2 (2018), 243-288.

Dates
Revised: 15 September 2016
Accepted: 20 September 2016
First available in Project Euclid: 3 March 2018

https://projecteuclid.org/euclid.kjm/1520046287

Digital Object Identifier
doi:10.1215/21562261-2017-0023

Mathematical Reviews number (MathSciNet)
MR3799703

Zentralblatt MATH identifier
06896955

#### Citation

Odaka, Yuji. Canonical Kähler metrics and arithmetics: Generalizing Faltings heights. Kyoto J. Math. 58 (2018), no. 2, 243--288. doi:10.1215/21562261-2017-0023. https://projecteuclid.org/euclid.kjm/1520046287

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