Timeline for Group over algebraic curves having genus greater than 1
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 24, 2018 at 22:40 | vote | accept | Alm | ||
| Jul 24, 2018 at 22:40 | vote | accept | Alm | ||
| Jul 24, 2018 at 22:40 | |||||
| Jul 23, 2018 at 20:22 | vote | accept | Alm | ||
| Jul 24, 2018 at 22:40 | |||||
| Jul 21, 2018 at 7:29 | answer | added | Bombyx mori | timeline score: 1 | |
| Jul 19, 2018 at 19:48 | comment | added | Watson | Possibly related: math.stackexchange.com/questions/369723 | |
| Jul 19, 2018 at 8:23 | comment | added | Alm | Good point. Let me add that the multiplication law should be a rational function. | |
| Jul 19, 2018 at 8:21 | answer | added | Ben McKay | timeline score: 5 | |
| Jul 19, 2018 at 8:12 | answer | added | user19475 | timeline score: 18 | |
| Jul 19, 2018 at 8:05 | answer | added | Francesco Polizzi | timeline score: 12 | |
| Jul 19, 2018 at 8:01 | answer | added | jmc | timeline score: 7 | |
| Jul 19, 2018 at 7:54 | comment | added | jmc | By the way: there exist elliptic curves over the rationals that have finitely many rational points. | |
| Jul 19, 2018 at 7:53 | comment | added | jmc | Every non-empty set can be endowed with a group structure. But that is not (should not be?) what you are after. I do not see why you would be interested in putting a group structure on the rational points of some variety if you don't ask for some compatibility with the geometric structure. (It is like have a set, endowing it with a group structure and a topology, but not caring whether multiplication is continuous...) | |
| Jul 19, 2018 at 7:47 | comment | added | user19475 | You could also look at the tangent bundle or use the Lefschetz fixed point formula applied to the translation by the unit section. | |
| Jul 19, 2018 at 7:46 | comment | added | Alm | Does this property not hold for curves with genus greater than 1? In the case, one could have a group over the rationals that is not compatible with group over extended fields. At least in principle. | |
| Jul 19, 2018 at 7:20 | comment | added | Qiaochu Yuan | It's not just that there's a group structure on the rational points; e.g. there's a group structure on the points over any field extension $K$ of the ground field, and these group structures are compatible with inclusions of field extensions. More precisely, elliptic curves are what are called group schemes. | |
| Jul 19, 2018 at 7:20 | comment | added | KConrad | A curve of genus $g\geq 1$has an associated group (abelian variety), its Jacobian variety, of dimension $g$. For $g>1$ the Jacobian is not a curve. | |
| Jul 19, 2018 at 7:15 | history | asked | Alm | CC BY-SA 4.0 |