Timeline for Parahoric group schemes over curves
Current License: CC BY-SA 3.0
4 events
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| Aug 16, 2014 at 18:14 | comment | added | rvarma | hi thank you , yes i am aware of the patching result you mentioned above and hence suspected the inclusion $B \subset \mathcal{G}(X)$. When all the parahorics under consideration are inside $G(\mathcal{O}_x)$,we have a map $\mathcal{G} \rightarrow C \times G$,so is it the case that $\mathcal{G}(X) \subset G$? | |
| Aug 16, 2014 at 17:37 | comment | added | user54268 | For any Dedekind scheme $X$ and dense open $U \subset X$, an $X$-affine scheme $Y$ is "the same" as a $U$-affine scheme $Y'$ and $\widehat{O}_{X,x}$-schemes $Y'_x$ equipped with identifications with the generic fiber of $Y'$ over ${\rm{Frac}}(\widehat{O}_{X,x})$. This interacts well with smoothness, group scheme structure, etc. See Prop. D4(b) in section 6.2 of "Neron models". Hence, you can pre-assign whatever you want over each $\widehat{O}_{X,x}$. So using the "same" $B$ at each $x \in X-U$ does the job. This is why the real content of Bruhat-Tits theory is in the local case. | |
| Aug 16, 2014 at 16:12 | history | edited | rvarma | CC BY-SA 3.0 |
deleted 2 characters in body
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| Aug 16, 2014 at 14:48 | history | asked | rvarma | CC BY-SA 3.0 |