Restriction of sheaf on a closed subscheme is in general not quasi-coherent?

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In Hartshorne 5.2.4, we have




If $Y$ is a closed subscheme of a scheme $X$, then the sheaf $mathcalO_Y$ is not in general quasi-coherent in $Y$.




I'm having a hard time believing this, mainly because I can't think of any examples. Would any affine $X$ make an example? Say we have the closed subscheme $Y = textSpec A/mathfraka$ embedded in $X = textSpec A$.



Thanks!




algebraic-geometry sheaf-theory




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    As Hartshorne points out, it isn't even an $mathcal O_Y$-module in general: $A$ is typically not an $A/mathfrak a$-module
    – John Brevik
    Aug 27 at 20:10














up vote
0
down vote

favorite
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In Hartshorne 5.2.4, we have




If $Y$ is a closed subscheme of a scheme $X$, then the sheaf $mathcalO_Y$ is not in general quasi-coherent in $Y$.




I'm having a hard time believing this, mainly because I can't think of any examples. Would any affine $X$ make an example? Say we have the closed subscheme $Y = textSpec A/mathfraka$ embedded in $X = textSpec A$.



Thanks!




algebraic-geometry sheaf-theory




share|cite|improve this question
















  • 3




    As Hartshorne points out, it isn't even an $mathcal O_Y$-module in general: $A$ is typically not an $A/mathfrak a$-module
    – John Brevik
    Aug 27 at 20:10












up vote
0
down vote

favorite
1









up vote
0
down vote

favorite
1






1





In Hartshorne 5.2.4, we have




If $Y$ is a closed subscheme of a scheme $X$, then the sheaf $mathcalO_Y$ is not in general quasi-coherent in $Y$.




I'm having a hard time believing this, mainly because I can't think of any examples. Would any affine $X$ make an example? Say we have the closed subscheme $Y = textSpec A/mathfraka$ embedded in $X = textSpec A$.



Thanks!




algebraic-geometry sheaf-theory




share|cite|improve this question












In Hartshorne 5.2.4, we have




If $Y$ is a closed subscheme of a scheme $X$, then the sheaf $mathcalO_Y$ is not in general quasi-coherent in $Y$.




I'm having a hard time believing this, mainly because I can't think of any examples. Would any affine $X$ make an example? Say we have the closed subscheme $Y = textSpec A/mathfraka$ embedded in $X = textSpec A$.



Thanks!





algebraic-geometry sheaf-theory





share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 27 at 14:46









nekodesu

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  • 3




    As Hartshorne points out, it isn't even an $mathcal O_Y$-module in general: $A$ is typically not an $A/mathfrak a$-module
    – John Brevik
    Aug 27 at 20:10












  • 3




    As Hartshorne points out, it isn't even an $mathcal O_Y$-module in general: $A$ is typically not an $A/mathfrak a$-module
    – John Brevik
    Aug 27 at 20:10







3




3




As Hartshorne points out, it isn't even an $mathcal O_Y$-module in general: $A$ is typically not an $A/mathfrak a$-module
– John Brevik
Aug 27 at 20:10




As Hartshorne points out, it isn't even an $mathcal O_Y$-module in general: $A$ is typically not an $A/mathfrak a$-module
– John Brevik
Aug 27 at 20:10















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