Timeline for Realization Functor From $SH$ to Derived Category of $Gal$-Modules
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 21, 2015 at 20:08 | comment | added | Marc Hoyois | @MikhailBondarko If $S$ is excellent and $p$ is invertible on $S$, then for every strictly henselian local ring $A$ of $S$ and every $x\in Spec(A)$, $cd_p(\kappa(x))=dim(\overline{\{x\}})<\infty$. This finiteness condition, for all $p$ dividing $n$, is the assumption of Ayoub's rigidity theorem. | |
| Nov 21, 2015 at 19:29 | comment | added | Mikhail Bondarko | Are you sure that Ayoub did not demand any finiteness of l-adic cohomological dimension restrictions? | |
| Nov 21, 2015 at 2:19 | comment | added | Marc Hoyois | I should add, it's only a technical matter to make $p\mapsto p_!p^!\Lambda$ into an (op?)lax symmetric monoidal functor, and it is known to be strict symmetric monoidal when $S$ is excellent, by work of Gabber. When $S$ is a field, however, this was proved by Deligne in SGA4½. | |
| Nov 21, 2015 at 1:22 | vote | accept | Elden Elmanto | ||
| Nov 21, 2015 at 1:16 | history | answered | Marc Hoyois | CC BY-SA 3.0 |