Timeline for In what sense is the complex $\mathscr{L}^\bullet$ unique?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 13, 2023 at 3:18 | vote | accept | Yikun Qiao | ||
| Jun 29, 2023 at 11:45 | answer | added | Leo Alonso | timeline score: 2 | |
| Jun 29, 2023 at 10:26 | comment | added | Jason Starr | The discussion of this in Chapter 2 of Mumford's "Abelian varieties" is particularly short and clear. I usually tell students to skip that section of Hartshorne's book and read it instead in Mumford's book. | |
| Jun 29, 2023 at 9:32 | comment | added | R. van Dobben de Bruyn | In particular, see [Tag 0B91 (2)] for existence of the 'Grothendieck complex' $\mathscr L^{\bullet}$ (using [Tags 08EB and 0657] for translation to the case where the base $Y$ is affine). | |
| Jun 29, 2023 at 5:51 | comment | added | abx | $\mathscr{L}^{\bullet}=Rf_*\mathscr{F}$, an object of the (bounded) derived category $D(Y)$. The nontrivial point is that it is a perfect object in $D(Y)$, commuting with base change. You can have a look at chapter 36 in the Stacks project. | |
| Jun 29, 2023 at 3:20 | history | asked | Yikun Qiao | CC BY-SA 4.0 |