Timeline for Twisted line bundles Brauer class
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jan 8, 2017 at 17:34 | comment | added | Sasha | @Libli: As Jason said, the class $p^*\alpha$ is trivial. On the other hand, the category of (untwisted) sheaves on $Y$ that restrict as a multiplicity of $O(1)$ to each fiber over $X$ is equivalent to the category of $\alpha$-twisted sheaves on $X$. All this, I believe, is explained in a paper of Bernardara "A semiorthogonal decomposition for Brauer-Severi schemes". | |
| Jan 8, 2017 at 17:15 | comment | added | Libli | @JasonStarr : so if the class $p^* \alpha$ is trivial, this means that $\mathcal{O}_{Y/X}(1)$ is a true line bundle? It seems quite strange... | |
| Jan 8, 2017 at 14:08 | comment | added | Jason Starr | The class $p^*\alpha$ is trivial. | |
| Jan 8, 2017 at 13:32 | comment | added | Libli | thanks a lot for your answer! So just to be sure I understood, in the case of a Severi Brauer variety, the "rank" of $\mathcal{O}_{Y/X}(1)$ would be the rank of $E$ (where $E$ is the twisted vector bundle which defines $Y$). Furthermore the class $p^* \alpha$ is non-trivial and its order is the rank of $E$. Is that correct? | |
| Jan 8, 2017 at 13:17 | history | answered | Sasha | CC BY-SA 3.0 |