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March 2020 Hyperbolicity Notions for Varieties Defined over a Non-Archimedean Field
R. Rodríguez Vázquez
Michigan Math. J. 69(1): 41-78 (March 2020). DOI: 10.1307/mmj/1574326880

Abstract

Firstly, we pursue the work of W. Cherry on the analogue of the Kobayashi semidistance dCK, which he introduced for analytic spaces defined over a non-Archimedean metrized field k. We prove various characterizations of smooth projective varieties for which dCK is an actual distance.

Secondly, we explore several notions of hyperbolicity for a smooth algebraic curve X defined over k. We prove a non-Archimedean analogue of the equivalence between having a negative Euler characteristic and the normality of certain families of analytic maps taking values in X.

Citation

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R. Rodríguez Vázquez. "Hyperbolicity Notions for Varieties Defined over a Non-Archimedean Field." Michigan Math. J. 69 (1) 41 - 78, March 2020. https://doi.org/10.1307/mmj/1574326880

Information

Received: 3 January 2018; Revised: 29 August 2018; Published: March 2020
First available in Project Euclid: 21 November 2019

zbMATH: 07208925
MathSciNet: MR4071345
Digital Object Identifier: 10.1307/mmj/1574326880

Subjects:
Primary: 32P05
Secondary: 32H02

Rights: Copyright © 2020 The University of Michigan

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Vol.69 • No. 1 • March 2020
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