Stein domains in Banach algebraic geometry |
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Authors: | Federico Bambozzi Oren Ben-Bassat Kobi Kremnizer |
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Institution: | 1. Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany;2. Mathematical Institute, Department of Mathematics, University of Haifa, Haifa, Israel;3. Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK |
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Abstract: | In this article we give a homological characterization of the topology of Stein spaces over any valued base field. In particular, when working over the field of complex numbers, we obtain a characterization of the usual Euclidean (transcendental) topology of complex analytic spaces. For non-Archimedean base fields the topology we characterize coincides with the topology of the Berkovich analytic space associated to a non-Archimedean Stein algebra. Because the characterization we used is borrowed from a definition in derived geometry, this work should be read as a derived perspective on analytic geometry. |
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Keywords: | Stein space Berkovich space Bornological space Nuclear space |
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