  In the framework of the collinear factorized pQCD approach we calculate the
small-$x_B$ process-dependent nuclear modification to the structure functions
measured in neutrino-nucleus deeply inelastic scattering. We include both heavy
quark mass corrections $(M^2/Q^2)$ and resummed nuclear-enhanced dynamical
power corrections in the quantity $(\xi^2/Q^2)(A^{1/3}-1)$ with $\xi^2$
evaluated to leading order in $\alpha_s$. Our formalism predicts a measurable
difference in the shadowing pattern of the structure functions $F_2^A(x_B,Q^2)$
and $F_3^A(x_B,Q^2)$ and a significant low- and moderate-$Q^2$ modification of
the QCD sum rules. We also comment on the relevance of our results to the NuTeV
extraction of $\sin^2\theta_W$.
