Timeline for My first question - on Affine Schemes in Algebraic Geometry
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 28, 2012 at 9:01 | vote | accept | Christopher Townsend | ||
| Feb 28, 2012 at 9:01 | |||||
| Feb 28, 2012 at 9:01 | vote | accept | Christopher Townsend | ||
| Feb 28, 2012 at 9:01 | |||||
| Feb 23, 2012 at 15:36 | comment | added | Keenan Kidwell | I wish it were always taken as the definition of an affine scheme. | |
| Feb 23, 2012 at 14:17 | comment | added | Martin Brandenburg | This is well-known (EGA I, 1.6.3). Sometimes this is also taken as the definition of an affine scheme (Demazure-Gabriel). | |
| Feb 23, 2012 at 13:29 | comment | added | Keenan Kidwell | This fact also gives (what I think is) a nice characterization of affineness among all locally ringed spaces. If $Y$ is a locally ringed space, taking $X=\mathrm{Spec}(\mathscr{O}_Y(Y))$ in Sasha's answer shows there is a unique morphism $f:Y→\mathrm{Spec}(\mathscr{O}Y(Y))$ inducing the identity on global sections, and $Y$ is an affine scheme (in the sense that it is isomorphic to the spectrum of some ring via some isomorphism) if and only if this canonical $f$ is an isomorphism. | |
| Feb 23, 2012 at 9:29 | history | answered | Sasha | CC BY-SA 3.0 |