A non-Archimedean Ohsawa-Takegoshi extension theorem

Abstract

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

20 pages. Simplified the proof of Lemma 3.7 and added a new proof of Lemma 4.13, minor changes. To appear in Math Z