Timeline for Homotopy invariance of $\ell$-adic cohomology
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 10, 2022 at 13:24 | vote | accept | Gabriel | ||
| May 9, 2022 at 15:48 | comment | added | Swann | About axiom 2 : cohomological purity implies that $s^!p^*\Lambda \simeq \Lambda(-1)[-2]$ (Milne's étale cohomology , theorem 6.1). We even have (by remark 5.2 in loc. cit.) that for any locally constant étale $\Lambda$-sheaf $F$ on $S$, $s^!p^*F \simeq F\otimes\Lambda(-1)$, therefore the functor $s^!p^*$ coincides with twisting by (-1). It is natural to ask that twisting is invertible, and as $p_\sharp s_*$ is left adjoint to $s^!p^*$ it also equal its inverse, thus condition 2 is ''twisting by 1 is an invertible functor''. | |
| May 9, 2022 at 12:36 | answer | added | Will Sawin | timeline score: 8 | |
| May 9, 2022 at 11:51 | history | asked | Gabriel | CC BY-SA 4.0 |