Timeline for How can we generalize the finite type property so that global sections still have the same property?
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Feb 19, 2021 at 20:37 | comment | added | Jason Starr | For every scheme with this property, the total ring of fractions is essentially of finite type. | |
| Feb 19, 2021 at 19:36 | comment | added | Tim Campion | An example of a variety whose ring of global sections is not finitely-generated is given in Vakil's Foundations of Algebraic Geometry, Exercise 19.11.13. If I were to go out on a limb, I'd guess that $Spec k[x_1,x_2,\dots]$ is in $\mathbf F$, and therefore that $Spec R$ is in $\mathbf F$ for any countably-generated $k$-algebra $R$, so that any scheme admitting a finite open cover by $Spec R$'s where $R$ is countably generated, is in $\mathbf F$, and maybe that's exactly what $\mathbf F$ is? | |
| Feb 19, 2021 at 18:52 | history | asked | Gro-Tsen | CC BY-SA 4.0 |