Timeline for Example of an integral scheme which is geometrically connected but not geometrically irreducible
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 24, 2017 at 21:50 | vote | accept | dorebell | ||
| Aug 24, 2017 at 15:08 | review | Close votes | |||
| Aug 25, 2017 at 9:10 | |||||
| Aug 24, 2017 at 13:29 | answer | added | Jason Starr | timeline score: 5 | |
| Aug 24, 2017 at 4:02 | comment | added | dorebell | Thanks, Jason! If you'll submit this as an answer, I'll accept it. | |
| Aug 22, 2017 at 10:44 | comment | added | Jason Starr | For the field $\mathbb{R}$, the affine $\mathbb{R}$-scheme $\text{Spec} \ \mathbb{R}[x,y]/\langle x^2+y^2\rangle$ is integral and geometrically connected, but it is not geometrically irreducible. If $X_k$ is an integral, locally finite type $k$-scheme that is geometrically connected and normal, then $X_{\overline{k}}$ is irreducible. For geometric irreduciblity it is irrelevant whether $k$ is perfect: the field extension $\overline{k}/k^{\text{sep}}$ is a universal homeomorphism. However, perfectness is relevant for reducedness. | |
| Aug 22, 2017 at 10:34 | history | asked | dorebell | CC BY-SA 3.0 |