Geodesic
The set of points at which a morphism of affine schemes is not finite
Zbigniew Jelonek 1   ; Marek Kara/s 2
1 Zbigniew Jelonek Institute of Mathematics Polish Academy of Sciences Św. Tomasza 30 31-027 Kraków, Poland
2 Institute 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
Colloquium Mathematicum, Tome 92 (2002) no. 1, pp. 59-66 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm92-1-5
Keywords: assume integral noetherian affine schemes rightarrow dominant generically finite morphism finite type set points which morphism finite either empty hypersurface example given longer non noetherian

Zbigniew Jelonek  1   ; Marek Kara/s  2

1 Zbigniew Jelonek Institute of Mathematics Polish Academy of Sciences Św. Tomasza 30 31-027 Kraków, Poland
2 Institute 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 
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Zbigniew Jelonek; Marek Kara/s. The set of points at which a morphism of affine
schemes is not finite. Colloquium Mathematicum, Tome 92 (2002) no. 1, pp. 59-66. doi: 10.4064/cm92-1-5

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