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A non-Archimedean Ohsawa–Takegoshi extension theorem

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Abstract

We prove an Ohsawa–Takegoshi-type extension theorem on the Berkovich closed unit disc over certain non-Archimedean fields. As an application, we establish a non-Archimedean analogue of Demailly’s regularization theorem for quasisubharmonic functions on the Berkovich unit disc.

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Notes

  1. If \(\Gamma \) is a subtree of X that contains \(x_G\), we adopt the following conventions: if \(\Gamma \supsetneq \{ x_G \}\), then \({{\mathrm{Ends}}}(\Gamma )\) consists of those points in \(\Gamma \) with a unique tangent direction in \(\Gamma \); if \(\Gamma = \{ x_G \}\), then \({{\mathrm{Ends}}}(\Gamma ) = \Gamma \).

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Acknowledgements

I would like to thank my advisor, Mattias Jonsson, for suggesting the problem and for his invaluable help, guidance, and support. I would also like to thank Kiran Kedlaya, Jérôme Poineau, and Daniele Turchetti for helpful conversations regarding Lemma 2.1. I am grateful to Takumi Murayama and Emanuel Reinecke for their many comments on a previous draft. Finally, I would like to thank the anonymous referee for their many helpful comments, and for pointing out an error in a previous version. This work was partially supported by NSF grant DMS-1600011.

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  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1043, USA

    Matthew Stevenson

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  1. Matthew Stevenson
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Correspondence to Matthew Stevenson.

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Stevenson, M. A non-Archimedean Ohsawa–Takegoshi extension theorem. Math. Z. 291, 279–302 (2019). https://doi.org/10.1007/s00209-018-2083-4

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  • DOI: https://doi.org/10.1007/s00209-018-2083-4

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