Stein domains in Banach algebraic geometry

Federico Bambozzi, Oren Ben-Bassat, Kobi Kremnizer

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)1865-1927
Number of pages63
JournalJournal of Functional Analysis
Issue number7
StatePublished - 1 Apr 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.


  • Berkovich space
  • Bornological space
  • Nuclear space
  • Stein space

ASJC Scopus subject areas

  • Analysis


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