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</script>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.
Local ground fields in algebraic geometry, 510.mathematics, SPACES, sheaves, rigid space, affinoid space over a complete nonarchimedean field, Article, Arithmetic algebraic geometry (Diophantine geometry), points
Local ground fields in algebraic geometry, 510.mathematics, SPACES, sheaves, rigid space, affinoid space over a complete nonarchimedean field, Article, Arithmetic algebraic geometry (Diophantine geometry), points
| citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 27 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
