  Let X be a smooth variety over a field k, and l be a prime number invertible
in k. We study the (\'etale) unramified H^3 of X with coefficients Q_l/Z_l(2)
in the style of Colliot-Th\'el\`ene and Voisin. If k is separably closed,
finite or p-adic, this describes it as an extension of a finite group F by a
divisible group D, where F is the torsion subgroup of the cokernel of the
l-adic cycle map. If k is finite and X is projective and of abelian type,
verifying the Tate conjecture, D=0. If k is separably closed, we relate D to an
l-adic Griffiths group. If k is the separable closure of a finite field and X
comes from a variety over a finite field as described above, then D = 0 as soon
as H^3(X,Q_l) is entirely of coniveau > 0, but an example of Schoen shows that
this condition is not necessary.
