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The set of points at which a morphism of affine schemes is not finite

Tom 92 / 2002

Zbigniew Jelonek, Marek Kara/s Colloquium Mathematicum 92 (2002), 59-66 MSC: 14E10, 14E22, 14E40. DOI: 10.4064/cm92-1-5

Streszczenie

Assume that $X,Y$ are integral noetherian affine schemes. Let $f:X\rightarrow Y$ be a dominant, generically finite morphism of finite type. We show that the set of points at which the morphism $f$ is not finite is either empty or a hypersurface. An example is given to show that this is no longer true in the non-noetherian case.

Autorzy

  • Zbigniew JelonekZbigniew Jelonek
    Institute of Mathematics
    Polish Academy of Sciences
    Św. Tomasza 30
    31-027 Kraków, Poland
    e-mail
  • Marek Kara/sInstitute of Mathematics
    Polish Academy of Sciences
    /Sw. Tomasza 30
    31-027 Krak/ow, Poland
    and
    Institute of Mathematics
    Jagiellonian University
    Reymonta 4
    30-059 Krak/ow, Poland
    e-mail

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