Isolated types of finite rank: an abstract Dixmier–Moeglin equivalence

• Omar León Sánchez ^[1] ; Rahim Moosa ^[2]
  1. [1] University of Manchester

     University of Manchester

     Reino Unido

     
  2. [2] University of Waterloo

     University of Waterloo

     Canadá

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 1, 2019
• Idioma: inglés
• DOI: 10.1007/s00029-019-0450-6
• Enlaces
  • Texto completo (pdf)
• Resumen

  • Suppose T is a totally transcendental first-order theory and every minimal non-locally-modular type is nonorthogonal to a nonisolated minimal type over the empty set. It is shown that a finite rank type p=tp(a/A) is isolated if and only if Open image in new window for every b∈acl(Aa) and q∈S(Ab) nonisolated and minimal. This applies to the theory of differentially closed fields—where it is motivated by the differential Dixmier–Moeglin equivalence problem—and the theory of compact complex manifolds.