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A new proof of the Gerritzen-Grauert theorem. (English) Zbl 1080.32021
The Gerritzen-Grauert theorem [see, for example, S. Bosch, U. Güntzer and R. Remmert, Non-Archimedean analysis. A systematic approach to rigid analytic geometry (1984; Zbl 0539.14017)] is one of the most fundamental results of rigid analitic geometry. It describes locally closed immersions between affinoid varieties, and this description implies the fact that any affinoid variety is a finite union of rational domains. The latter is used in the computations of Čech cohomology for affinoid varieties, and also in Berkovich’s non-Archimedean analytic geometry.
The author gives a new proof of the Gerritzen-Grauert theorem, more elementary than the known ones and allowing a generalization from the rigid analytic geometry based on the class of strictly affinoid algebras to the case of arbitrary affinoid algebras.

MSC:
32P05 Non-Archimedean analysis
14G22 Rigid analytic geometry
32C99 Analytic spaces
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