Timeline for Torsors in Algebraic Geometry?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 6, 2010 at 5:51 | comment | added | user8248 | Stupid Question: What's the non-cech H^1 when G is non-abelian? | |
| Mar 27, 2010 at 14:48 | vote | accept | Chris Schommer-Pries | ||
| Mar 27, 2010 at 14:48 | comment | added | Chris Schommer-Pries | Thanks Brian! I think Martin's answer together with Brian's example from Raynaud's thesis constitutes a fully acceptable answer. I find this subtle question quite fascinating! | |
| Mar 27, 2010 at 3:01 | comment | added | BCnrd | See XIII, 3.2 in Raynaud's thesis (SLN 119). It involves $S$ normal local noetherian of dimension 2, and $G$ an abelian scheme over $S$. Basically the simplest possible situation, since $G$ cannot be $S$-affine and algebraic space torsors for abelian schemes over a Dedekind base are always quasi-projective schemes (see "Neron Models" book). Raynaud's example is an fppf sheaf torsor (so an algebraic space, by Artin's theory) which is not a scheme. | |
| Mar 26, 2010 at 16:18 | comment | added | Martin Bright | Not offhand, and I think any such example has to be fairly hairy. According to Milne there are some given by Raynaud in Faisceaux Amples sur les Schémas en Groupes et les Espaces Homogènes, Springer LNM 119. | |
| Mar 26, 2010 at 15:35 | comment | added | Chris Schommer-Pries | I'll take a closer look at Milne's book, but in the meantime you don't know an example where the two notions of torsor differ, do you? | |
| Mar 26, 2010 at 15:02 | history | answered | Martin Bright | CC BY-SA 2.5 |