Analytic functions on tubes of non-Archimedean analytic spaces
Abstract
Let be a discretely valued non-Archimedean field. We give an explicit description of analytic functions whose norm is bounded by a given real number on tubes of reduced -analytic spaces associated to special formal schemes (those include -affinoid spaces as well as open polydiscs). As an application we study the connectedness of these tubes. This generalizes (in the discretely valued case) a result of Siegfried Bosch. We use as a main tool a result of A.J. de Jong relating formal and analytic functions on special formal schemes and a generalization of de Jong's result which is proved in the joint appendix with Christian Kappen.
Keywords
Cite
@article{arxiv.1510.01178,
title = {Analytic functions on tubes of non-Archimedean analytic spaces},
author = {Florent Martin and Christian Kappen},
journal= {arXiv preprint arXiv:1510.01178},
year = {2017}
}
Comments
19 pages; modifications in section 4 to drop the assumption that the rings are reduced; typos corrected and examples added; the appendix appears now as a joint appendix