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We evaluate nuclear shadowing of the total cross section of charm particlesproduction in DIS within the framework of the Gribov theory of nuclearshadowing using as input the recent QCD Pomeron parton density analysis of theHERA diffractive data. Assuming that the QCD factorization theorem isapplicable to the charm production off nuclei we also calculate shadowing ofthe 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 thephysics of heavy ion collisions at LHC. We also discuss some properties of thefinal states for $\gamma^*A $ processes dominated by the scattering off small$x$ gluons like the high $p_t$ jet and charm production.Comment: 20 pages, 5 figure

Diffractive production of charm in DIS and gluon nuclear shadowing