Timeline for Base change in Chriss-Ginzburg
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 16 at 20:58 | vote | accept | Yellow Pig | ||
| Aug 16 at 20:23 | comment | added | Sasha | If you want a map to be defined on the Grothendieck group, you should define the pullback as the alternating sum of derived functors. But the derived functors are not trivial in this case. | |
| Aug 16 at 20:11 | comment | added | Yellow Pig | Sorry, also I don't understand your counterexample: if $Z=\tilde Z = \tilde S$ then $\psi^* f_*$ is identity anyway because the sheaf does not change on $\tilde S$ under these operations, so I don't see anything wrong with base change in this case. | |
| Aug 16 at 19:52 | comment | added | Sasha | As I mentioned, you can look to the book of Lipman for the very general case where base change works. A simpler setup is also discussed in Section 2.4 of [Kuznetsov, A. G. Hyperplane sections and derived categories. Izv. Math. 70 (2006), no. 3, 447–547], (see in particular Corollary 2.27). | |
| Aug 16 at 19:47 | comment | added | Yellow Pig | Thank you! Is there a similar base change statement to (b) which is correct? Also, I am not familiar with any books by Lipman, how do I find this book? Did you mean that the book by Lipman has something similar to (b) which is correct? | |
| Aug 16 at 19:16 | history | answered | Sasha | CC BY-SA 4.0 |