Proper Morphism with Finite Fibers is Finite
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Let $f: X to Y$ a morphism between schemes. I'm looking for a reference / sketch for the proof that is $f$ proper amd has finite fibers then $f$ is already finite.
Can the proof redicaly simplified if we assume that $X,Y$ a curves, so $1$-dimensional, proper $k$-schemes?
algebraic-geometry schemes
asked Dec 30 '18 at 3:54
KarlPeterKarlPeter
6921315
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add a comment |
$begingroup$
Let $f: X to Y$ a morphism between schemes. I'm looking for a reference / sketch for the proof that is $f$ proper amd has finite fibers then $f$ is already finite.
Can the proof redicaly simplified if we assume that $X,Y$ a curves, so $1$-dimensional, proper $k$-schemes?
algebraic-geometry schemes
asked Dec 30 '18 at 3:54
KarlPeterKarlPeter
6921315
$endgroup$
1
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stacks.math.columbia.edu/tag/02OG
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– loch
Dec 30 '18 at 4:10
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Theorem 29.6.2 in Vakil's notes
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– Bananeen
Dec 30 '18 at 7:51
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There is a more elementary proof for projective morphisms (which includes the special case of curves you are interested in); see [Liu, Exercise 4.4.2] or [Stacks, footnote in Tag 0A27].
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– Takumi Murayama
Dec 31 '18 at 20:50
add a comment |
$begingroup$
Let $f: X to Y$ a morphism between schemes. I'm looking for a reference / sketch for the proof that is $f$ proper amd has finite fibers then $f$ is already finite.
Can the proof redicaly simplified if we assume that $X,Y$ a curves, so $1$-dimensional, proper $k$-schemes?
algebraic-geometry schemes
asked Dec 30 '18 at 3:54
KarlPeterKarlPeter
6921315
$endgroup$
Let $f: X to Y$ a morphism between schemes. I'm looking for a reference / sketch for the proof that is $f$ proper amd has finite fibers then $f$ is already finite.
Can the proof redicaly simplified if we assume that $X,Y$ a curves, so $1$-dimensional, proper $k$-schemes?
algebraic-geometry schemes
algebraic-geometry schemes
asked Dec 30 '18 at 3:54
KarlPeterKarlPeter
6921315
asked Dec 30 '18 at 3:54
KarlPeterKarlPeter
6921315
asked Dec 30 '18 at 3:54
KarlPeterKarlPeter
6921315
asked Dec 30 '18 at 3:54
KarlPeterKarlPeter
6921315
asked Dec 30 '18 at 3:54
KarlPeterKarlPeter
6921315
6921315
1
$begingroup$
stacks.math.columbia.edu/tag/02OG
$endgroup$
– loch
Dec 30 '18 at 4:10
$begingroup$
Theorem 29.6.2 in Vakil's notes
$endgroup$
– Bananeen
Dec 30 '18 at 7:51
$begingroup$
There is a more elementary proof for projective morphisms (which includes the special case of curves you are interested in); see [Liu, Exercise 4.4.2] or [Stacks, footnote in Tag 0A27].
$endgroup$
– Takumi Murayama
Dec 31 '18 at 20:50
add a comment |
1
$begingroup$
stacks.math.columbia.edu/tag/02OG
$endgroup$
– loch
Dec 30 '18 at 4:10
$begingroup$
Theorem 29.6.2 in Vakil's notes
$endgroup$
– Bananeen
Dec 30 '18 at 7:51
$begingroup$
There is a more elementary proof for projective morphisms (which includes the special case of curves you are interested in); see [Liu, Exercise 4.4.2] or [Stacks, footnote in Tag 0A27].
$endgroup$
– Takumi Murayama
Dec 31 '18 at 20:50
1
1
$begingroup$
stacks.math.columbia.edu/tag/02OG
$endgroup$
– loch
Dec 30 '18 at 4:10
$begingroup$
stacks.math.columbia.edu/tag/02OG
$endgroup$
– loch
Dec 30 '18 at 4:10
$begingroup$
Theorem 29.6.2 in Vakil's notes
$endgroup$
– Bananeen
Dec 30 '18 at 7:51
$begingroup$
Theorem 29.6.2 in Vakil's notes
$endgroup$
– Bananeen
Dec 30 '18 at 7:51
$begingroup$
There is a more elementary proof for projective morphisms (which includes the special case of curves you are interested in); see [Liu, Exercise 4.4.2] or [Stacks, footnote in Tag 0A27].
$endgroup$
– Takumi Murayama
Dec 31 '18 at 20:50
$begingroup$
There is a more elementary proof for projective morphisms (which includes the special case of curves you are interested in); see [Liu, Exercise 4.4.2] or [Stacks, footnote in Tag 0A27].
$endgroup$
– Takumi Murayama
Dec 31 '18 at 20:50
add a comment |
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1
$begingroup$
stacks.math.columbia.edu/tag/02OG
$endgroup$
– loch
Dec 30 '18 at 4:10
$begingroup$
Theorem 29.6.2 in Vakil's notes
$endgroup$
– Bananeen
Dec 30 '18 at 7:51
$begingroup$
There is a more elementary proof for projective morphisms (which includes the special case of curves you are interested in); see [Liu, Exercise 4.4.2] or [Stacks, footnote in Tag 0A27].
$endgroup$
– Takumi Murayama
Dec 31 '18 at 20:50