Mild manifolds and a non-standard Riemann existence theorem

Ya'Acov Peterzil, Sergei Starchenko

Research output: Contribution to journalArticlepeer-review

Abstract

Let R be an o-minimal expansion of a real closed field R, and K be the algebraic closure of R. In earlier papers we investigated the notions of R-definable K-holomorphic maps, K-analytic manifolds and their K-analytic subsets. We call such a K-manifold mild if it eliminates quantifers after endowing it with all it K-analytic subsets. Examples are compact complex manifolds and non-singular algebraic curves over K. We examine here basic properties of mild manifolds and prove that when a mild manifold M is strongly minimal and not locally modular then it is biholomorphic to a non-singular algebraic curve over K.

Original languageEnglish
Pages (from-to)275-298
Number of pages24
JournalSelecta Mathematica, New Series
Volume14
Issue number2
DOIs
StatePublished - Jan 2009

Bibliographical note

Funding Information:
We would like to thank Elias Baro for pointing out a gap in one of the proofs. The second author was partially supported by the NSF.

Keywords

  • Non-Archimedean complex analysis
  • O-minimality
  • Riemann existence theorem
  • Zariski geometries

ASJC Scopus subject areas

  • Mathematics (all)
  • Physics and Astronomy (all)

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