Timeline for Artin's "On isolated rational singularities of surfaces"
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| S Dec 30, 2020 at 22:00 | history | bounty ended | CommunityBot | ||
| S Dec 30, 2020 at 22:00 | history | notice removed | CommunityBot | ||
| Dec 28, 2020 at 21:55 | history | edited | user267839 | CC BY-SA 4.0 |
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| Dec 22, 2020 at 21:04 | history | edited | YCor | CC BY-SA 4.0 |
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| Dec 22, 2020 at 20:39 | history | edited | user267839 | CC BY-SA 4.0 |
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| S Dec 22, 2020 at 20:15 | history | bounty started | user267839 | ||
| S Dec 22, 2020 at 20:15 | history | notice added | user267839 | Canonical answer required | |
| Dec 22, 2020 at 20:14 | history | edited | user267839 | CC BY-SA 4.0 |
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| S Feb 21, 2020 at 3:03 | history | bounty ended | CommunityBot | ||
| S Feb 21, 2020 at 3:03 | history | notice removed | CommunityBot | ||
| S Feb 13, 2020 at 1:34 | history | bounty started | user267839 | ||
| S Feb 13, 2020 at 1:34 | history | notice added | user267839 | Canonical answer required | |
| Feb 13, 2020 at 1:34 | comment | added | user267839 | That is that $H^0$ and $\otimes$ commute. I'm facing two problems now: first one: to show that $m O_V$ is invertible $O_V$-module. (then it would flat and $H^0$ and $\otimes$ commute and we are done). The second problem is the initial induction step: how to show that $A/m \to H^0(Z,O_{Z})$ is surjection? | |
| Feb 13, 2020 at 1:33 | comment | added | user267839 | I think I have (almost) the answer I was looking for: The problem is to show that $a$ surjective and by induction hypothesis $c_n: A/m^k \to H^0(Z,O_{kZ})$ is surjective for all $k < n+1$. Assume $A/m \to H^0(Z,O_{Z})$ is surjective (that's a seriuos problem: see below problem 2, but let at first assume we know it). We tensor it with $m^n$ and obtain the surjection $m^n/m^{n+1} \to m^n \otimes H^0(V, K_n)$. The goal would be to show $m^n \otimes H^0(Z,O_{Z})= H^0(V, K_n)$. | |
| S Feb 10, 2020 at 6:41 | history | suggested | AG learner | CC BY-SA 4.0 |
typo correction
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| Feb 9, 2020 at 18:28 | review | Suggested edits | |||
| S Feb 10, 2020 at 6:41 | |||||
| Feb 9, 2020 at 3:00 | comment | added | user267839 | I think that it was just a typo in the paper. That is we consider indeed $A/{\mathfrak m}^n\to H^0(nZ,O_{nZ})$ induced canonically by $nZ \subset V \to \bar{V}=Spec(A)$ on the ring side ($A \to H^0(nZ,O_{nZ})$ factorizes through $A/{\mathfrak m}^n$) | |
| Feb 8, 2020 at 11:24 | comment | added | inkspot | I don't know whether this will answer the question, but you write $A/{\mathfrak m}^n\to H^0(nZ,O_{nZ})$ while Artin's homomorphism goes in the opposite direction. | |
| Feb 8, 2020 at 0:51 | history | asked | user267839 | CC BY-SA 4.0 |