Timeline for Quotient of abelian variety by an abelian subvariety
Current License: CC BY-SA 2.5
4 events
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| Sep 3, 2010 at 13:08 | comment | added | B. Cais | Hey Brian, and thanks for your thoughts. I now agree that one has to use some things which are not "trivial", whether it be representability of alg. space quotients or Poincare reducibility or properties of $\mathcal{E}xt(\cdot,\mathbb{G}_m)$, as in my comment to Francesco's answer below. | |
| Sep 2, 2010 at 21:48 | answer | added | Francesco Polizzi | timeline score: 18 | |
| Sep 2, 2010 at 21:13 | comment | added | BCnrd | Hey Bryden, non-affine quotient existence results by action of something more than a finite flat group probably cannot be entirely "easy", since one cannot easily see where the coordinate rings on the quotient are to come from. Within the framework of algebraic spaces one can make good quotients in great generality (it is the method to use in general when the base is not an artin ring), and then sometimes prove the alg. space quotient is a scheme (e.g., alg. space group lft over field is scheme...); sometimes qt isn't a scheme! In your case, trick via Poincare red. seems simplest (to me). | |
| Sep 2, 2010 at 20:26 | history | asked | B. Cais | CC BY-SA 2.5 |