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December 2021 Adelic Cartier divisors with base conditions and the continuity of volumes
Hideaki Ikoma
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Kyoto J. Math. 61(4): 905-947 (December 2021). DOI: 10.1215/21562261-2021-0018

Abstract

We propose an extended notion of adelic R-Cartier divisors, called 1-adelic R-Cartier divisors, which enables us to associate a Banach space to each algebraic variety over the field of rational numbers, and establish the global continuity of the arithmetic volume function defined on the space of pairs of 1-adelic R-Cartier divisors and R-base conditions.

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Hideaki Ikoma. "Adelic Cartier divisors with base conditions and the continuity of volumes." Kyoto J. Math. 61 (4) 905 - 947, December 2021. https://doi.org/10.1215/21562261-2021-0018

Information

Received: 5 September 2018; Revised: 30 June 2019; Accepted: 19 July 2019; Published: December 2021
First available in Project Euclid: 20 October 2021

Digital Object Identifier: 10.1215/21562261-2021-0018

Subjects:
Primary: 14G40
Secondary: 11G50

Keywords: adelic divisors , Arakelov theory , arithmetic volumes , base conditions , continuity

Rights: Copyright © 2021 by Kyoto University

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Vol.61 • No. 4 • December 2021
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