Timeline for Can we classify reductive group schemes over curves
Current License: CC BY-SA 3.0
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Sep 25, 2014 at 8:23 | comment | added | User12345 | There is also this paper: link.springer.com/article/10.1007%2FBF01425451 | |
| Sep 25, 2014 at 8:21 | comment | added | User12345 | Is it Harder, G.: Halbeinfache Gruppenschemata über Dedekindringen. Inventiones math.4, 165–191 (1967) ? I will take a look at it. | |
| Sep 25, 2014 at 2:28 | comment | added | user27920 | There is an old paper by Harder (in German) which I believe does the most one can hope for over a general connected Dedekind base, but I don't remember the reference; maybe someone else does. | |
| Sep 25, 2014 at 2:27 | comment | added | user27920 | The most interesting case is that of semisimple groups. Over any scheme $S$, every rank-$n$ vector bundle $E$ on $S$ gives rise to the Zariski-form ${\rm{SL}}(E)$ of ${\rm{SL}}_n$, and every rank-$n$ fiberwise non-degenerate line-bundle valued quadratic space $q:V \rightarrow L$ over $S$ (with $n \ge 3$) gives rise to the $S$-group ${\rm{SO}}(q)$ (whose isomorphism class encodes the isomorphism class of $(V,L,q)$ up to ${\rm{Pic}}(S)$-twisting), so it's hard to know what you might mean by a "concrete description", especially over a non-complete curve. | |
| Sep 24, 2014 at 22:46 | comment | added | S. Carnahan♦ | You get an $n$-torus for any conjugacy class of homomorphisms $\pi_1^{et}(C) \to \mathrm{GL}_n(\mathbb{Z})$. | |
| Sep 24, 2014 at 22:09 | review | First posts | |||
| Sep 24, 2014 at 22:23 | |||||
| Sep 24, 2014 at 22:09 | history | asked | User12345 | CC BY-SA 3.0 |