Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 58, Number 2 (2018), 243-288.
Canonical Kähler metrics and arithmetics: Generalizing Faltings heights
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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
Received: 4 October 2015
Revised: 15 September 2016
Accepted: 20 September 2016
First available in Project Euclid: 3 March 2018
Permanent link to this document
https://projecteuclid.org/euclid.kjm/1520046287
Digital Object Identifier
doi:10.1215/21562261-2017-0023
Mathematical Reviews number (MathSciNet)
MR3799703
Zentralblatt MATH identifier
06896955
Subjects
Primary: 14G40: Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]
Keywords
Faltings heights Kähler–Einstein metrics Arakelov geometry
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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