Points and topologies in rigid geometry
type: Item
instance of: scholarly article
title: Points and topologies in rigid geometry
zbMATH Open document ID: 0867.11049
DOI: 10.1007/BF01444488
author: M. van der Put
author: Peter Schneider
published in: Mathematische Annalen
publication date: 1997-02-01T00:00:00Z
full work available at URL: https://eudml.org/doc/165324
review text: Let \(X\) be an affinoid space over a complete nonarchimedean field. The usual points of \(X\) are not sufficient to investigate sheaves on \(X\); for instance, there exist sheaves of \({\mathcal O}_{\mathcal X}\)-modules with all stalks equal to (0) and which are not (0). A main question is ``to add points'' to obtain a topoï with sufficiently many points. Preceeding works in that direction have been made by \textit{M. van der Put} [Compos. Math. 45, 165-198 (1982; Zbl 0491.14014)], \textit{V. G. Berkovich} [Math. Surveys Monographs 33, Am. Math. Soc. (1990; Zbl 0715.14013) and Publ. Math., Inst. Hautes Étud. Sci. 78, 5-161 (1993; Zbl 0804.32019)], \textit{R. Huber} [Math. Z. 212, 455-477 (1993; Zbl 0788.13010)] and \textit{P. Schneider} [J. Reine Angew. Math. 434, 127-157 (1993; Zbl 0774.14021)]. The purpose of this paper is to clarify the various concepts of points. Indeed, a link between Huber's approach and Berkovich's is given, which works for points and sheaves.
Mathematics Subject Classification ID: 11G99
Mathematics Subject Classification ID: 14G20
zbMATH DE Number: 769470
zbMATH Keywords: rigid space
zbMATH Keywords: points
zbMATH Keywords: sheaves
zbMATH Keywords: affinoid space over a complete nonarchimedean field
reviewed by: Marc Reversat
MaRDI profile type: Publication
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OpenAlex ID: W1998913330
description: scientific article; zbMATH DE number 769470