We evaluate nuclear shadowing of the total cross section of charm particles production in DIS within the framework of Gribov theory of nuclear shadowing generalized to account for the QCD evolution. We use as an 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 large for heavy nuclei: GA∼200(x, Q2)/AGN(x, Q2) ∼ 0.45-0.5 · (A/200)-0.15 for x ∼ 10-3÷-4, Q2 ∼ 20 ÷ 40GeV2 to influence significantly the physics of heavy ion collisions at LHC. We evaluate also suppression of minijet and hidden charm production in the central AA collisions. We also discuss some properties of the final states for γ*A processes dominated by the scattering off small x gluons like the high pt jet and charm production.