Dagger geometry as Banach algebraic geometry

Federico Bambozzi, Oren Ben-Bassat

Research output: Contribution to journalArticlepeer-review


In this article, we look at analytic geometry from the perspective of relative algebraic geometry with respect to the categories of bornological and Ind-Banach spaces over valued fields (both Archimedean and non-Archimedean). We are able to recast the theory of Grosse-Klönne dagger affinoid domains with their weak G-topology in this new language. We prove an abstract recognition principle for the generators of their standard topology (the morphisms appearing in the covers) and for the condition of a family of morphisms to be a cover. We end with a sketch of an emerging theory of dagger affinoid spaces over the integers, or any Banach ring, where we can see the Archimedean and non-Archimedean worlds coming together.

Original languageEnglish
Pages (from-to)391-462
Number of pages72
JournalJournal of Number Theory
StatePublished - 1 May 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.


  • Global analytic geometry
  • Over-convergent structure sheaf
  • Rigid geometry

ASJC Scopus subject areas

  • Algebra and Number Theory


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