ScalingStacks

For each prime $\ell$ invertible in $k$, there is an $\ell$-adic realisation functor to the category $\operatorname{D}(X,\mathbb{Q}_{\ell})$ of $\ell$-adic sheaves on $X$

(3.1)

$\displaystyle\operatorname{Real}_{\ell}:\operatorname{DM}(X,\mathbb{Q})\to\operatorname{D}(X,\mathbb{Q}_{\ell}),$

which is compatible with the six functors and the Tate twist, see [Ayo14].