Arc-meromorphous functions

Wojciech Kucharz, Krzysztof Kurdyka Annales Polonici Mathematici MSC: 14P10, 14P20, 32B10, 58A07. DOI: 10.4064/ap200517-7-8 Published online: 30 September 2020


We introduce arc-meromorphous functions, which are continuous functions representable as quotients of semialgebraic arc-analytic functions, and develop the theory of arc-meromorphous sheaves on Nash manifolds. Our main results are Cartan’s theorems A and B for quasi-coherent arc-meromorphous sheaves.


  • Wojciech KucharzInstitute of Mathematics
    Faculty of Mathematics
    and Computer Science
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland
  • Krzysztof KurdykaUniv. Savoie Mont Blanc
    CNRS UMR 5127 LAMA
    73000 Chambéry, France

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