Analytic functions on tubes of nonarchimedean analytic spaces

Abstract

Let $k$ be a discretely valued nonarchimedean field. We give an explicit description of analytic functions whose norm is bounded by a given real number $r$ on tubes of reduced $k$-analytic spaces associated to special formal schemes (including $k$-affinoid spaces as well as open polydiscs). As an application we study the connectedness of these tubes. In the discretely valued case, this generalizes a result of Siegfried Bosch. We use as a main tool a result of Aise Johan 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.