Timeline for When does glueing affine schemes produce affine/separated schemes?
Current License: CC BY-SA 4.0
10 events
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| Aug 5, 2019 at 18:34 | history | edited | Minseon Shin | CC BY-SA 4.0 |
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| Aug 1, 2019 at 6:51 | comment | added | Minseon Shin | The description I had in mind was as the semi-local ring of two points $\{0,\infty\}$ in $\mathbb{P}_{k}^{1}$. After applying the automorphism of $\mathbb{P}_{k}^{1}$ sending $\{0,\infty\}$ to $\{0,1\}$, it is isomorphic to the intersection of $k[x]_{(x)}$ and $k[x]_{(x-1)}$ inside $k(x)$. | |
| Aug 1, 2019 at 6:24 | comment | added | Minseon Shin | Hi @rbarc, I don't think that's a correct description of the ring of global functions; for example it's not closed under addition (e.g. consider $\frac{x+1}{1}-\frac{1}{1}$) | |
| Jul 12, 2019 at 8:14 | comment | added | Minseon Shin | Yup :/ maybe someone else can find an example. | |
| Jul 12, 2019 at 7:38 | comment | added | user142965 | do I understand correctly that you don't know an example where this procedure gives a separated non-affine scheme (for a DVR)? | |
| Jul 12, 2019 at 6:30 | comment | added | Minseon Shin | For me $k(x) := \operatorname{Frac}(k[x])$, namely the field of rational functions in the variable $x$ over $k$. | |
| Jul 12, 2019 at 5:51 | comment | added | user142965 | what is $k(x)$ in your answer? I believe formal Laurent series are infinite only in one direction so there is no automorphism $x\rightarrow \frac{1}{x}$? | |
| Jul 12, 2019 at 5:10 | vote | accept | CommunityBot | ||
| Jul 11, 2019 at 22:27 | history | edited | Minseon Shin | CC BY-SA 4.0 |
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| Jul 11, 2019 at 21:44 | history | answered | Minseon Shin | CC BY-SA 4.0 |