  We evaluate nuclear shadowing of the total cross section of charm particles
production in DIS within the framework of the Gribov theory of nuclear
shadowing using as input the recent QCD Pomeron parton density analysis of the
HERA diffractive data. Assuming that the QCD factorization theorem is
applicable to the charm production off nuclei we also calculate shadowing of
the gluon densities in nuclei and find it sufficiently larg for heavy nuclei:
$G_{A\sim 200}(x,Q^2)/AG_N(x,Q^2) \sim 0.45-0.5 \cdot (A/200)^{-0.15}$ for $x
\sim 10^{-3\div -4}, Q^2 \sim 10 \div 40 GeV^2$ to influence significantly the
physics of heavy ion collisions at LHC. We also discuss some properties of the
final states for $\gamma^*A $ processes dominated by the scattering off small
$x$ gluons like the high $p_t$ jet and charm production.
