Analytic functions on tubes of non-Archimedean analytic spaces

摘要

Let $k$ be a discretely valued non-Archimedean field. We give an explicitdescription of analytic functions whose norm is bounded by a given real number$r$ on tubes of reduced $k$-analytic spaces associated to special formalschemes (those include $k$-affinoid spaces as well as open polydiscs). As anapplication we study the connectedness of these tubes. This generalizes (in thediscretely valued case) a result of Siegfried Bosch. We use as a main tool aresult of A.J. de Jong relating formal and analytic functions on special formalschemes and a generalization of de Jong's result which is proved in the jointappendix with Christian Kappen.