Timeline for Chow groups and short exact sequence
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 27, 2013 at 16:03 | comment | added | Jason Starr | @StevenLandsburg: Okay, now I see what you mean. | |
| Nov 27, 2013 at 14:44 | comment | added | Steven Landsburg | @JasonStarr: Yes, given that $X$ and $Y$ are closed, the problem is completely trivial unless $M$ is reducible, which is why I said in my earlier comment that the OP can and should drop the assumption that $M$ is smooth. For $M$ reducible the problem is still very easy but (though I wavered back and forth on this) I thought it was worth pointing out the simple argument that the OP might have missed. | |
| Nov 27, 2013 at 11:49 | comment | added | Jason Starr | @StevenLandsburg: I guess I am confused. For me a "variety" is an irreducible, finite type scheme over some (fixed) field. So if $M$ is a smooth projective variety, if $X$ and $Y$ are closed subsets, and if $M$ equals $X\cup Y$, then one of $X$ or $Y$ equals $M$, say $X=M$. Then the sequence is ridiculous. My suspicion is that, actually, the OP does not know quite what he wants to ask, he has written something a bit absurd, and the readers are struggling to project some meaning on what is written. | |
| Nov 27, 2013 at 6:07 | comment | added | Steven Landsburg | @JasonStarr: Actually, Fulton (quite reasonably) states this result without proof, so if the OP doesn't already see how to prove it, Fulton won't help. | |
| Nov 27, 2013 at 6:05 | answer | added | Steven Landsburg | timeline score: 3 | |
| Nov 26, 2013 at 23:10 | comment | added | Bryan261 | Yes, $ X $ and $ Y $ are closed. Thank you. | |
| Nov 26, 2013 at 23:07 | comment | added | Steven Landsburg | Do you mean to assume (per Jason Starr's comment) that $X$ and $Y$ are closed? If so, you can (and should!) drop the assumption that $M$ is smooth. | |
| Nov 26, 2013 at 21:59 | comment | added | Jason Starr | How are the maps in your sequence defined? "Proper pushforward" requires <I>proper</I> morphisms. I recommend that you read the introductory chapters of a good book on intersection theory, e.g., Fulton's book. | |
| Nov 26, 2013 at 21:51 | history | asked | Bryan261 | CC BY-SA 3.0 |