Timeline for Rationality of algebraic groups
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 3, 2012 at 22:58 | history | edited | Ryan Reich | CC BY-SA 3.0 |
hypotheses
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| Mar 3, 2012 at 22:20 | comment | added | S. Carnahan♦ | I think this only peoves geometric rationality - you may need the group to be quasi-split to invoke Bruhat over the ground field. | |
| Mar 3, 2012 at 22:11 | comment | added | Ryan Reich | (I consider the larger class to be just "group schemes") | |
| Mar 3, 2012 at 22:10 | comment | added | Ryan Reich | Sorry, I keep forgetting that "algebraic group" means something different to some people. I have in mind only affine algebraic groups. | |
| Mar 3, 2012 at 22:06 | comment | added | Allen Knutson | The Bruhat decomposition is usually stated for affine reductive groups, unlike this elliptic curve. | |
| Mar 3, 2012 at 21:56 | comment | added | Qiaochu Yuan | By "rationality" shouldn't we also mean that the group multiplication, inverse, and identity are defined over $\mathbb{Q}$? In that case, an elliptic curve whose $j$-invariant isn't rational can't be rational, right? | |
| Mar 3, 2012 at 21:32 | history | answered | Ryan Reich | CC BY-SA 3.0 |