Timeline for a question about abelian scheme
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 16, 2012 at 16:42 | answer | added | Xandi Tuni | timeline score: 3 | |
| Jan 16, 2012 at 15:37 | history | edited | kiseki | CC BY-SA 3.0 |
added 24 characters in body
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| Jan 16, 2012 at 15:13 | comment | added | S. Carnahan♦ | Martin is pointing out that when one says "elliptic curve" or "abelian variety" one is including the datum of an identity section. In particular, an easy counterexample comes from choosing an elliptic curve $X$ over a trait $S$, and changing the identity section (and hence the group law) in the closed fiber. The identity sections over the two points cannot be glued to a single identity section from $S$ to $X$. You can fix this problem by forgetting about the identity section, and asking for $X$ to be a torsor under some abelian scheme. | |
| Jan 16, 2012 at 13:45 | comment | added | kiseki | Yes,Martin.I hope there is a group structure on X which compatible with the group structure on the fibres. | |
| Jan 16, 2012 at 13:39 | comment | added | S. Carnahan♦ | Perhaps you should ask if you get a torsor under an $S$-group scheme. | |
| Jan 16, 2012 at 13:32 | comment | added | Martin Bright | I think you need to be a bit careful here: are you looking for a group structure on $X$ which induces the ones you already have on the fibres? Because, unless I'm confused, you can make this impossible even for a trivial family of elliptic curves simply by choosing different base points in each fibre. | |
| Jan 16, 2012 at 12:46 | history | asked | kiseki | CC BY-SA 3.0 |