Let $k$ be a field, $l$ be a prime number invertible in $k$, $X/k$ be an algebraic variety, then the triangulated category $D_c^b(X)$ of bounded constructible complexes of étale $\mathbb{Q}_l$-sheaves plays an important role when defining perverse sheaves (and in various other applications). But I find its definition so complicated that I don't know what it is concretely.
For the simplest case $X=\mathrm{Spec}(k)$, we know that a constructible sheaf on $X$ is lisse, hence an object of $Rep_{\mathbb{Q}_l}(\Gamma_k)$ (the abelian category of finite dimensional continuous $\mathbb{Q}_l$-representations of the absolute Galois group $\Gamma_k$). There is a triangulated functor $D^b(Rep_{\mathbb{Q}_l}(\Gamma_k))\to D_c^b(k)$. Is it always an equivalence?
For example, when the cohomological dimension of $k$ is $\le 1$, it is true. But what if $k$ is a number field?