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arXiv · 1801.02479

Hyperbolicity notions for varieties defined over a non-Archimedean field

Rita Rodríguez Vázquez
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Abstract

Firstly, we pursue the work of W. Cherry on the analogue of the Kobayashi semi distance dCK that 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 negative Euler characteristic and the normality of certain families of analytic maps taking values in X.

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Rita Rodríguez Vázquez. 2018-01-08. Hyperbolicity notions for varieties defined over a non-Archimedean field. https://arxiv.org/abs/1801.02479

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