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June 2018 Canonical Kähler metrics and arithmetics: Generalizing Faltings heights
Yuji Odaka
Kyoto J. Math. 58(2): 243-288 (June 2018). DOI: 10.1215/21562261-2017-0023

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.

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Yuji Odaka. "Canonical Kähler metrics and arithmetics: Generalizing Faltings heights." Kyoto J. Math. 58 (2) 243 - 288, June 2018. https://doi.org/10.1215/21562261-2017-0023

Information

Received: 4 October 2015; Revised: 15 September 2016; Accepted: 20 September 2016; Published: June 2018
First available in Project Euclid: 3 March 2018

zbMATH: 06896955
MathSciNet: MR3799703
Digital Object Identifier: 10.1215/21562261-2017-0023

Subjects:
Primary: 14G40

Rights: Copyright © 2018 Kyoto University

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Vol.58 • No. 2 • June 2018
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