Rational maps induced by natural transformations
I am reading the paper Function Spaces and Continuos Algebraic Pairings for Varieties of Friedlander and Walker. More precisely, I am working on the following result.
In the proof of the proposition the authors claim that a natural transformation as above determines a rational map by sending a generic point $etacolon mathsf{Spec} , Flongrightarrow X$ to $Phi_f(eta)colonmathsf{Spec} , Flongrightarrow Y$. This passage is clear, indeed there is bijective correspondence between the rational maps from $X$ to $Y$ and morphisms
from $mathsf{Spec} , F $ to $Y$.
What I would to know is if the same thing holds true in the setup of classical quasi-projective varaieties, that is, open subsets of zero loci (in some projective space) of homogeneous polynomials. Of course in this case one cannot use the same argumet as above, because we don't have generic points. Any idea?
algebraic-geometry
asked Nov 29 '18 at 1:31
Vincenzo ZaccaroVincenzo Zaccaro
1,239719
add a comment |
I am reading the paper Function Spaces and Continuos Algebraic Pairings for Varieties of Friedlander and Walker. More precisely, I am working on the following result.
In the proof of the proposition the authors claim that a natural transformation as above determines a rational map by sending a generic point $etacolon mathsf{Spec} , Flongrightarrow X$ to $Phi_f(eta)colonmathsf{Spec} , Flongrightarrow Y$. This passage is clear, indeed there is bijective correspondence between the rational maps from $X$ to $Y$ and morphisms
from $mathsf{Spec} , F $ to $Y$.
What I would to know is if the same thing holds true in the setup of classical quasi-projective varaieties, that is, open subsets of zero loci (in some projective space) of homogeneous polynomials. Of course in this case one cannot use the same argumet as above, because we don't have generic points. Any idea?
algebraic-geometry
asked Nov 29 '18 at 1:31
Vincenzo ZaccaroVincenzo Zaccaro
1,239719
add a comment |
I am reading the paper Function Spaces and Continuos Algebraic Pairings for Varieties of Friedlander and Walker. More precisely, I am working on the following result.
In the proof of the proposition the authors claim that a natural transformation as above determines a rational map by sending a generic point $etacolon mathsf{Spec} , Flongrightarrow X$ to $Phi_f(eta)colonmathsf{Spec} , Flongrightarrow Y$. This passage is clear, indeed there is bijective correspondence between the rational maps from $X$ to $Y$ and morphisms
from $mathsf{Spec} , F $ to $Y$.
What I would to know is if the same thing holds true in the setup of classical quasi-projective varaieties, that is, open subsets of zero loci (in some projective space) of homogeneous polynomials. Of course in this case one cannot use the same argumet as above, because we don't have generic points. Any idea?
algebraic-geometry
asked Nov 29 '18 at 1:31
Vincenzo ZaccaroVincenzo Zaccaro
1,239719
I am reading the paper Function Spaces and Continuos Algebraic Pairings for Varieties of Friedlander and Walker. More precisely, I am working on the following result.
In the proof of the proposition the authors claim that a natural transformation as above determines a rational map by sending a generic point $etacolon mathsf{Spec} , Flongrightarrow X$ to $Phi_f(eta)colonmathsf{Spec} , Flongrightarrow Y$. This passage is clear, indeed there is bijective correspondence between the rational maps from $X$ to $Y$ and morphisms
from $mathsf{Spec} , F $ to $Y$.
What I would to know is if the same thing holds true in the setup of classical quasi-projective varaieties, that is, open subsets of zero loci (in some projective space) of homogeneous polynomials. Of course in this case one cannot use the same argumet as above, because we don't have generic points. Any idea?
algebraic-geometry
algebraic-geometry
asked Nov 29 '18 at 1:31
Vincenzo ZaccaroVincenzo Zaccaro
1,239719
asked Nov 29 '18 at 1:31
Vincenzo ZaccaroVincenzo Zaccaro
1,239719
asked Nov 29 '18 at 1:31
Vincenzo ZaccaroVincenzo Zaccaro
1,239719
asked Nov 29 '18 at 1:31
Vincenzo ZaccaroVincenzo Zaccaro
1,239719
asked Nov 29 '18 at 1:31
Vincenzo ZaccaroVincenzo Zaccaro
1,239719
1,239719
add a comment |
add a comment |
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