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2017 Analytic functions on tubes of nonarchimedean analytic spaces
Florent Martin
Algebra Number Theory 11(3): 657-683 (2017). DOI: 10.2140/ant.2017.11.657

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.

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Florent Martin. "Analytic functions on tubes of nonarchimedean analytic spaces." Algebra Number Theory 11 (3) 657 - 683, 2017. https://doi.org/10.2140/ant.2017.11.657

Information

Received: 11 May 2016; Revised: 14 December 2016; Accepted: 11 January 2017; Published: 2017
First available in Project Euclid: 19 October 2017

zbMATH: 06722478
MathSciNet: MR3649364
Digital Object Identifier: 10.2140/ant.2017.11.657

Subjects:
Primary: 14G22
Secondary: 13F25, 13F40

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 3 • 2017
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