Interplay of Soft and Hard Interactions in Nuclear Shadowing at High   $Q^2$ and Low x
  Nuclear shadowing corrections are dominated by soft interaction and grow as function of $1/x$ more slowly than the single scattering term, which has an essential contribution from hard interaction. Therefore, we predict vanishing nuclear shadowing at very low $x$ provided that $Q^2$ is high and fixed. At the same time, at medium and low $Q^2$, nuclear shadowing grows with $1/x$ as is well known for soft hadronic interactions. 
B.Z. Kopeliovich and B. Povh (MPI Heidelberg)