Timeline for Subschemes in group action
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 8, 2018 at 22:21 | comment | added | Qfwfq | (I took the liberty to add the "positive characteristic" tag) | |
| May 8, 2018 at 22:20 | history | edited | Qfwfq |
edited tags
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| May 8, 2018 at 20:25 | vote | accept | Fuzuj | ||
| May 8, 2018 at 20:16 | answer | added | Jason Starr | timeline score: 3 | |
| May 8, 2018 at 18:58 | comment | added | Jason Starr | "I accidentally forgot the hypothesis $H$ is smooth. Is it true now?" In my example, $H$ is the $k$-scheme $\text{Spec}\ k$ with its unique structure of a group $k$-scheme, i.e., $H$ is the trivial group scheme. So requiring $H$ to be smooth does not change the conclusion. | |
| May 8, 2018 at 18:51 | history | edited | Fuzuj | CC BY-SA 4.0 |
added 44 characters in body
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| May 8, 2018 at 18:48 | comment | added | Fuzuj | I accidentally forgot the hypothesis $H$ smooth. Is it true now? | |
| May 8, 2018 at 17:38 | comment | added | Jason Starr | I believe this is false. The subgroup $k$-schemes of $G=\mathbb{G}_{a,k}^2$ isomorphic to $\alpha_{p,k}$ are parameterized by $\mathbb{P}^1_k$. Inside the group $\mathbb{P}^1_k$-scheme $\mathbb{P}^1_k \times \mathbb{G}_{a,k}^2$, let $\Gamma$ be the universal closed subgroup scheme that is finite and flat over $\mathbb{P}^1_k$ with geometric fibers isomorphic to $\alpha_p$. Denote the quotient by this subgroup scheme by $q:\mathbb{P}^1_k\times \mathbb{G}_{a,k}^2\to X$ with its induced action of $G=\mathbb{G}_{a,k}^2$. Let $Y$ be the identity section of the group $\mathbb{P}^1_k$-scheme $X$. | |
| May 8, 2018 at 15:36 | review | First posts | |||
| May 8, 2018 at 15:37 | |||||
| May 8, 2018 at 15:33 | history | asked | Fuzuj | CC BY-SA 4.0 |