Timeline for open subgroup scheme closed
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| Feb 25, 2016 at 14:38 | comment | added | nfdc23 | Among the interesting examples near the end of Raynaud’s thesis (Springer LNM 119) is a smooth affine group $G$ over $\mathbf{A}^2_k$ (${\rm{char}}(k)=0$) whose open relative identity component $G^0$ is shown to be not affine (even worse than not closed!): see (iii) in section 3 of Chapter VII. This is also optimal for being quasi-affine but not affine because any flat separated group scheme of finite type over a discrete valuation ring with affine generic fiber is affine: see Prop. 3.1 of the paper “On quasi-reductive group schemes” by G. Prasad and J-K Yu for Raynaud's proof of this fact. | |
| Feb 25, 2016 at 12:49 | history | answered | darx | CC BY-SA 3.0 |