  Let $k$ be a field of characteristic zero with a fixed embedding
$\sigma:k\hookrightarrow \mathbb{C}$ into the field of complex numbers. Given a
$k$-variety $X$, we use the triangulated category of \'etale motives with
rational coefficients on $X$ to construct an abelian category $\mathscr{M}(X)$
of perverse mixed motives. We show that over $\mathrm{Spec}(k)$ the category
obtained is canonically equivalent to the usual category of Nori motives and
that the derived categories $\mathrm{D}^{\mathrm{b}}(\mathscr{M}(X))$ are
equipped with the four operations of Grothendieck (for morphisms of
quasi-projective $k$-varieties) as well as nearby and vanishing cycles functors
and a formalism of weights.
  In particular, as an application, we show that many classical constructions
done with perverse sheaves, such as intersection cohomology groups or Leray
spectral sequences, are motivic and therefore compatible with Hodge theory.
This recovers and strengthens work by Zucker, Saito, Arapura and de
Cataldo-Migliorini and provide an arithmetic proof of the pureness of
intersection cohomology with coefficients in a geometric variation of Hodge
structures.
