Timeline for Defining path on the prime spectrum
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 26, 2021 at 20:50 | comment | added | Antoine Labelle | This is a duplicate of mathoverflow.net/q/379341/160416, which has an answer in comments | |
| Mar 26, 2021 at 19:32 | history | edited | David White | CC BY-SA 4.0 |
Fixed typos to this relatively new question
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| Mar 17, 2021 at 19:42 | comment | added | Peter Scholze | @AndreasBlass Oops, I'm sorry, you are of course right. But can you not build a version of this example that includes specializations back and forth? I think this ought to be a spectral space, still. | |
| Mar 17, 2021 at 17:51 | comment | added | Andreas Blass | @PeterScholze I don't (yet) understand your comment. In your example, isn't the partial order of prime ideals just a linear order, so every two ideals are joined by a zigzag (a single zig or a single zag)? | |
| Mar 17, 2021 at 15:55 | comment | added | Neil Strickland | There is a rich theory of homotopy types of finite non-Hausdorff spaces: see ncatlab.org/nlab/show/finite+topological+space for some references. Similar phenomena will appear if you study homotopy types of Zariski spectra of rings. | |
| Mar 17, 2021 at 14:38 | comment | added | Peter Scholze | @AndreasBlass That's not quite right. If $V$ is a valuation ring of infinite rank, you can have the situation $\mathrm{Spec}(V)=\{0,1,\ldots,\infty\}$ with the topology for which the open sets are all $\{n,n+1,\ldots,\infty\}$. In that case there is a map $[0,1]\to \mathrm{Spec}(V)$ connecting $0$ to $\infty$: On $[0,1/2]$, map to $0$, on $(1/2,3/4]$ map to $1$, on $(3/4,7/8]$ map to $2$ etc., finally mapping $1$ to $\infty$. | |
| Mar 17, 2021 at 12:27 | review | Close votes | |||
| Mar 23, 2021 at 3:01 | |||||
| Mar 15, 2021 at 18:22 | comment | added | Andreas Blass | The components (in the partial-order sense, i.e., equivalence classes of the "exists a zigzag" relation) of the partial order of prime ideals are open and closed in the Zariski topology, so the image of a continuous map from $[0,1]$ (or from any connected space) cannot meet more than one of them. | |
| Mar 15, 2021 at 13:47 | review | Low quality posts | |||
| Mar 16, 2021 at 8:50 | |||||
| Mar 15, 2021 at 13:16 | review | First posts | |||
| Mar 15, 2021 at 13:47 | |||||
| Mar 15, 2021 at 13:15 | history | asked | Anderias. C. D | CC BY-SA 4.0 |