Timeline for Dualizing sheaf on varieties
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 19, 2011 at 9:35 | vote | accept | Descartes | ||
| Aug 19, 2011 at 8:15 | answer | added | Ariyan Javanpeykar | timeline score: 7 | |
| Aug 18, 2011 at 22:26 | answer | added | Leo Alonso | timeline score: 7 | |
| Aug 18, 2011 at 19:43 | comment | added | the L | If a ring $A$ admits a dualizing complex, and $A \to B$ is smooth of relative dimension $n$, then you can obtain a dualizing complex on $B$ by tensoring with $\Omega^n_{B/A}$. | |
| Aug 18, 2011 at 19:04 | comment | added | Karl Schwede | Grothendieck duality and base change I think is the title. | |
| Aug 18, 2011 at 18:38 | comment | added | Descartes | Ah, and which book by Conrad? | |
| Aug 18, 2011 at 18:37 | comment | added | Descartes | Very fine comment, ulrich; thanks a lot! | |
| Aug 18, 2011 at 17:28 | comment | added | naf | Another reference is the book "Introduction to Grothendieck duality theory" by Altman and Kleiman. | |
| Aug 18, 2011 at 16:34 | comment | added | Karl Schwede | Or you can see Residues and Duality. I should also point out that such statements should even be fine for smooth morphisms to things that aren't fields (probably Gorenstein local ring is ok, again see Residues or Brian Conrad's book) Finally, lets say that $X$ is normal (you can get away with a lot less, but lets assume this), then the reflexification/S2-ifiction of $\Omega_X^{n}$ is the dualizing sheaf. | |
| Aug 18, 2011 at 16:30 | comment | added | naf | Yes, this is true for a smooth projective variety over any field. It should be possible to rewrite Hartshorne's proofs to work in this case. | |
| Aug 18, 2011 at 15:54 | history | asked | Descartes | CC BY-SA 3.0 |