A new proof of the Gerritzen-Grauert theorem (Q2571040)

The Gerritzen-Grauert theorem [see, for example, \textit{S. Bosch, U. Güntzer} and \textit{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.