Analytic functions on tubes of non-Archimedean analytic spaces

Abstract

Let $k$ be a discretely valued non-Archimedean 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 (those include $k$-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.

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

References in corpus (2)

• A trace formula for rigid varieties, and motivic Weil generating series for formal schemes
• Sur les composantes connexes d'une famille d'espaces analytiques p-adiques

Cited by in corpus (3)

• Normalized Berkovich spaces and surface singularities
• Patching over Berkovich Curves and Quadratic Forms
• Galois descent of semi-affinoid spaces