  The main goal of this paper is to deduce (from a recent resolution of
singularities result of Gabber) the following fact: (effective) Chow motives
with $Z[1/p]$-coefficients over a perfect field $k$ of characteristic $p$
generate the category $DM^{eff}_{gm}[1/p]$ (of effective geometric Voevodsky's
motives with $Z[1/p]$-coefficients). It follows that $DM^{eff}_{gm}[1/p]$ could
be endowed with a Chow weight structure $w_{Chow}$ whose heart is
$Chow^{eff}[1/p]$ (weight structures were introduced in a preceding paper,
where the existence of $w_{Chow}$ for $DM^{eff}_{gm}Q$ was also proved). As
shown in previous papers, this statement immediately yields the existence of a
conservative weight complex functor $DM^{eff}_{gm}[1/p]\to
K^b(Chow^{eff}[1/p])$ (which induces an isomorphism on $K_0$-groups), as well
as the existence of canonical and functorial (Chow)-weight spectral sequences
and weight filtrations for any cohomology theory on $DM^{eff}_{gm}[1/p]$. We
also define a certain Chow t-structure for $DM_{-}^{eff}[1/p]$ and relate it
with unramified cohomology. To this end we study birational motives and
birational homotopy invariant sheaves with transfers.
