Vol. 11, No. 3, 2017

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Analytic functions on tubes of nonarchimedean analytic spaces

Florent Martin

Appendix: Christian Kappen and Florent Martin

Vol. 11 (2017), No. 3, 657–683
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.

Keywords
affinoid spaces, tubes, semiaffinoid, reduction
Mathematical Subject Classification 2010
Primary: 14G22
Secondary: 13F25, 13F40
Milestones
Received: 11 May 2016
Revised: 14 December 2016
Accepted: 11 January 2017
Published: 6 May 2017
Authors
Florent Martin
Fakultät für Mathematik
Universität Regensburg
D-93040 Regensburg
Germany
Christian Kappen
Universität Duisburg-Essen
Institut für Experimentelle Mathematik
Ellernstraße 29
D-45326 Essen
Germany
Florent Martin