Timeline for Why can projective varieties just have abelian group operations?
Current License: CC BY-SA 2.5
2 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 23, 2011 at 8:14 | comment | added | ACL | Since the title of the questions mentions <i>group operations</i>, it may be interesting to observe that this proof shows the more general result: let $G$ be an algebraic group acting faithfully on an algebraic variety, if $G$ has a fixed point, then $G$ is linear. (The same holds if $G$ is an abstract group of finite type, or in the analytic category and gives strong constraints to possible actions of lattices on varieties.) Take $G$ is a projective algebraic group and apply this to the action by conjugation of $G$: the quotient of $G$ by its center is linear and projective, hence trivial. | |
| Mar 21, 2011 at 13:23 | history | answered | Emerton | CC BY-SA 2.5 |