Timeline for Grothendieck-Verdier duality for affine morphisms
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 17, 2015 at 15:12 | vote | accept | Li Yutong | ||
| Jun 16, 2015 at 20:08 | comment | added | pbelmans | I just looked at page 86, and there he doesn't explicitly say that his varieties / schemes are projective. But later on in the context of Fourier--Mukai transforms everything is projective, so it turns out fine where he applies things. I guess he didn't want to be too elaborate on $f^\times$ and $f^!$ in this preliminary section... | |
| Jun 16, 2015 at 19:57 | comment | added | Li Yutong | Okay, I see.... | |
| Jun 16, 2015 at 19:56 | comment | added | pbelmans | All varieties in the book of Huybrechts are taken to be (smooth) projective, and all morphisms between these are projective themselves. So he didn't have to put in the properness, it is there to start with. | |
| Jun 16, 2015 at 17:57 | comment | added | pro | I humbly think that Huybrechts forgot a properness assumption, either on X and Y or f. To add to dracula's comment below: the right adjoint to $Rf_*$ exists pretty much always, purely for formal reasons. However, people often denote it by $f^\times$, as $f^!$ is reserved for the more sophisticated "twisted inverse image". The two $f^\times, f^!$ coincide when $f$ is proper. | |
| Jun 16, 2015 at 17:42 | answer | added | Count Dracula | timeline score: 2 | |
| Jun 16, 2015 at 15:16 | history | edited | Li Yutong | CC BY-SA 3.0 |
edited title
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| Jun 16, 2015 at 15:10 | history | asked | Li Yutong | CC BY-SA 3.0 |