Timeline for Stabilizers in abelian varieties are also abelian? reference request
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 6, 2022 at 7:27 | vote | accept | Lior Bary-Soroker | ||
| Apr 3, 2022 at 17:49 | history | became hot network question | |||
| Apr 3, 2022 at 13:27 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
typo in the title
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| Apr 3, 2022 at 13:24 | answer | added | R. van Dobben de Bruyn | timeline score: 5 | |
| Apr 3, 2022 at 10:24 | comment | added | ali | @LiorBary-Soroker the stabilizer is by definition a group, it is not hard to see that it is closed and you are in characteristic 0 so every group is smooth so the natural component is an abelian variety(smooth complete group variety). it is defined over $K$ if $X$ is defined over $K$. You can look at the milne book on group schemes to see a discocision of stabilizer | |
| Apr 3, 2022 at 10:04 | comment | added | Lior Bary-Soroker | Thanks @Chris. Do you know a reference to "the connected component of the stabilizer containing the identity will be an abelian subvariety, but I don't know whether it will be defined over 𝐾" | |
| Apr 3, 2022 at 9:52 | comment | added | Chris | There should be some connexity/irreducibility assumption on $X$, otherwise take $X$ to be the $n$-torsion points of $A$ for any $n$, and the stabilizer will be equal to $X$. In general, the connected component of the stabilizer containing the identity will be an abelian subvariety, but I don't know whether it will be defined over $K$. | |
| Apr 3, 2022 at 9:45 | history | asked | Lior Bary-Soroker | CC BY-SA 4.0 |