  We define a theory of etale motives over a noetherian scheme. This provides a
system of categories of complexes of motivic sheaves with integral coefficients
which is closed under the six operations of Grothendieck. The rational part of
these categories coincides with the triangulated categories of Beilinson
motives (and is thus strongly related to algebraic $K$-theory). We extend the
rigity theorem of Suslin and Voevodsky over a general base scheme. This can be
reformulated by saying that torsion etale motives essentially coincide with the
usual complexes of torsion etale sheaves (at least if we restrict ourselves to
torsion prime to the residue characteristics). As a consequence, we obtain the
expected results of absolute purity, of finiteness, and of Grothendieck duality
for etale motives with integral coefficients, by putting together their
counterparts for Beilinson motives and for torsion etale sheaves. Following
Thomason's insights, this also provides a conceptual and convenient
construction of the $\ell$-adic realization of motives, as the homotopy
$\ell$-completion functor.
