Topological analogue of Zariski's Main Theorem?
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Zariski's main theorem says that over a nice base, a quasi finite separated morphism admits an open immersion into a finite morphism.
The rough topological translation I have in mind is that over a compact base, a universally cloesd bundle (continuous map) whose fibers are finite and discrete in the total space can be openly immersed in some sort of ramified cover. In other words, we can nicely arrange the sporadically spread fibers.
However:
- I don't see how to do something like this topologically.
- My topological translation is probably way off.
I remember there are topological translations of milder versions in Mumford's red book, but I would like a topological analogue of the modern (linked) version.
What is the topological picture here?
algebraic-geometry commutative-algebra schemes affine-geometry
asked Nov 21 at 22:16
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Zariski's main theorem says that over a nice base, a quasi finite separated morphism admits an open immersion into a finite morphism.
The rough topological translation I have in mind is that over a compact base, a universally cloesd bundle (continuous map) whose fibers are finite and discrete in the total space can be openly immersed in some sort of ramified cover. In other words, we can nicely arrange the sporadically spread fibers.
However:
- I don't see how to do something like this topologically.
- My topological translation is probably way off.
I remember there are topological translations of milder versions in Mumford's red book, but I would like a topological analogue of the modern (linked) version.
What is the topological picture here?
algebraic-geometry commutative-algebra schemes affine-geometry
asked Nov 21 at 22:16
Arrow
5,11211445
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Zariski's main theorem says that over a nice base, a quasi finite separated morphism admits an open immersion into a finite morphism.
The rough topological translation I have in mind is that over a compact base, a universally cloesd bundle (continuous map) whose fibers are finite and discrete in the total space can be openly immersed in some sort of ramified cover. In other words, we can nicely arrange the sporadically spread fibers.
However:
- I don't see how to do something like this topologically.
- My topological translation is probably way off.
I remember there are topological translations of milder versions in Mumford's red book, but I would like a topological analogue of the modern (linked) version.
What is the topological picture here?
algebraic-geometry commutative-algebra schemes affine-geometry
asked Nov 21 at 22:16
Arrow
5,11211445
Zariski's main theorem says that over a nice base, a quasi finite separated morphism admits an open immersion into a finite morphism.
The rough topological translation I have in mind is that over a compact base, a universally cloesd bundle (continuous map) whose fibers are finite and discrete in the total space can be openly immersed in some sort of ramified cover. In other words, we can nicely arrange the sporadically spread fibers.
However:
- I don't see how to do something like this topologically.
- My topological translation is probably way off.
I remember there are topological translations of milder versions in Mumford's red book, but I would like a topological analogue of the modern (linked) version.
What is the topological picture here?
algebraic-geometry commutative-algebra schemes affine-geometry
algebraic-geometry commutative-algebra schemes affine-geometry
asked Nov 21 at 22:16
Arrow
5,11211445
asked Nov 21 at 22:16
Arrow
5,11211445
asked Nov 21 at 22:16
Arrow
5,11211445
asked Nov 21 at 22:16
Arrow
5,11211445
asked Nov 21 at 22:16
Arrow
5,11211445
5,11211445
add a comment |
add a comment |
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