Timeline for What is a "non-trivial" example of a commutative algebraic group over $\mathbb{C}$?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Nov 10, 2021 at 21:56 | comment | added | Damian Rössler | @JasonStarr. Quite - your example is the "universal" one. | |
| Nov 10, 2021 at 15:28 | comment | added | Jason Starr | Yes, I was trying to say what @DamianRoessler said. There are nontrivial invertible sheaves over Abelian varieties, and these give examples. There is even a “universal torsor” defined over the product of the Abelian variety with its relative $\text{Pic}^0$. | |
| Nov 10, 2021 at 15:01 | comment | added | Damian Rössler | Doesn't any line bundle on an abelian variety, which is algebraically equivalent to $0$ but not trivial give an example? (by taking the associated $\theta$ group). | |
| Nov 10, 2021 at 13:07 | comment | added | Gabriel | Dear @JasonStarr would you mind explaining more? | |
| Nov 10, 2021 at 11:06 | comment | added | Jason Starr | The total space of the universal torsor over the relative $\text{Pic}^0$ of any smooth projective variety with nontrivial Picard gives an example. | |
| Nov 9, 2021 at 15:15 | vote | accept | Gabriel | ||
| Nov 9, 2021 at 14:59 | comment | added | YCor | If you allow this to be split after passing to a finite covering, you can take $G_m$ times an elliptic curve and mod out by a nontrivial "diagonal" finite cyclic subgroup. Then it's not split (although a finite cover splits). This little game can't be performed with $G_a$. | |
| Nov 9, 2021 at 14:57 | history | edited | YCor | CC BY-SA 4.0 |
fixed assumption and fixed equality-> isomorphism
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| Nov 9, 2021 at 14:30 | answer | added | Will Sawin | timeline score: 18 | |
| Nov 9, 2021 at 14:22 | history | asked | Gabriel | CC BY-SA 4.0 |