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April 2016 Height of varieties over finitely generated fields
José Ignacio Burgos Gil, Patrice Philippon, Martín Sombra
Kyoto J. Math. 56(1): 13-32 (April 2016). DOI: 10.1215/21562261-3445138

Abstract

We show that the height of a variety over a finitely generated field of characteristic zero can be written as an integral of local heights over the set of places of the field. This allows us to apply our previous work on toric varieties and extend our combinatorial formulae for the height to compute some arithmetic intersection numbers of nontoric arithmetic varieties over the rational numbers.

Citation

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José Ignacio Burgos Gil. Patrice Philippon. Martín Sombra. "Height of varieties over finitely generated fields." Kyoto J. Math. 56 (1) 13 - 32, April 2016. https://doi.org/10.1215/21562261-3445138

Information

Received: 15 August 2014; Revised: 26 November 2014; Accepted: 1 December 2014; Published: April 2016
First available in Project Euclid: 15 March 2016

zbMATH: 1358.14021
MathSciNet: MR3479316
Digital Object Identifier: 10.1215/21562261-3445138

Subjects:
Primary: 14G40
Secondary: 11G50, 14M25

Rights: Copyright © 2016 Kyoto University

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Vol.56 • No. 1 • April 2016
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