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.
Original language | English |
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Pages (from-to) | 1865-1927 |
Number of pages | 63 |
Journal | Journal of Functional Analysis |
Volume | 274 |
Issue number | 7 |
DOIs | |
State | Published - 1 Apr 2018 |
Bibliographical note
Publisher Copyright:© 2018 Elsevier Inc.
Keywords
- Berkovich space
- Bornological space
- Nuclear space
- Stein space
ASJC Scopus subject areas
- Analysis