Timeline for Group scheme counterexample
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 5, 2014 at 3:52 | answer | added | S. Carnahan♦ | timeline score: 2 | |
| S Oct 5, 2014 at 2:53 | history | suggested | Tadashi |
Added counterexamples tag
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| Oct 5, 2014 at 2:43 | review | Suggested edits | |||
| S Oct 5, 2014 at 2:53 | |||||
| Sep 23, 2013 at 15:21 | comment | added | Tom De Medts | @Marguax: I think it's better to post this as an answer rather than a comment; this makes your post more visible and makes it clear that the question has been answered. | |
| Sep 23, 2013 at 3:02 | comment | added | Marguax | Let $S = {\rm{Spec}}(R)$ for a local normal noetherian domain $R$ of dimension $\ge 2$, with $s \in S$ the closed point, and let $H = (\mathbf{Z}/(2))_S$ be the constant finite etale $S$-group associated to $\mathbf{Z}/(2)$. The open subscheme $G$ complementary to the non-identity point in the closed fiber $H_s$ is an $S$-subgroup, and as a scheme it is a disjoint union of $S$ and $S-\{s\}$. Thus, it is not $S$-affine since it is not affine (as $S - \{s\}$ is not affine, due to the hypotheses on $R$). | |
| Sep 23, 2013 at 1:38 | history | asked | LMN | CC BY-SA 3.0 |