Timeline for Galois action on the derived category of $l$-adic sheaves
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Jun 26, 2011 at 15:43 | comment | added | Torsten Ekedahl | The answer is now yes, $\Gamma$ may be seen as a functori from $G$-sheaves to $G$-modules and one can define $R\Gamma(X,F)$ as its derived functor. It is easy to see that the forgetful functor from $G$-modules to modules takes this $R\Gamma(X,F)$ to the usual one (use Grothendieck's composite functor theorem). | |
| Jun 26, 2011 at 9:38 | comment | added | shenghao | By "$G$-equivariant $l$-adic sheaves" do you mean "$l$-adic $G$-modules"? Or you are working in the relative case $f:X\to Y$ and asking if $Rf_*F$ is a $G$-equiv. complex of sheaves on $Y$ (which has trivial $G$-action say)? | |
| Jun 26, 2011 at 6:23 | comment | added | Torsten Ekedahl | You have to have an action of $G$ also on $F$, i.e., a collection of maps $g^\ast F\to F$ fulfilling the obvious properties. In the case when $F$ is a constant sheaf there is automatically such an action but in general it is extra data. | |
| Jun 26, 2011 at 6:20 | history | asked | unknown | CC BY-SA 3.0 |