  We present a revision of predictions for nuclear shadowing in deep-inelastic
scattering at small Bjorken $x_{Bj}$ corresponding to kinematic regions
accessible by the future experiments at electron-ion colliders. The nuclear
shadowing is treated within the color dipole formalism based on the rigorous
Green function technique. This allows incorporating naturally color
transparency and coherence length effects, which are not consistently and
properly included in present calculations. For the lowest $|q\bar q\rangle$
Fock component of the photon, our calculations are based on an exact numerical
solution of the evolution equation for the Green function. Here the magnitude
of shadowing is tested using a realistic form for the nuclear density function,
as well as various phenomenological models for the dipole cross section. The
corresponding variation of the transverse size of the $q\bar q$ photon
fluctuations is important for $x_{Bj}\gtrsim 10^{-4}$, on the contrary with the
most of other models, which use frequently only the eikonal approximation with
the "frozen" transverse size. At $x_{Bj}\lesssim 0.01$ we calculate within the
same formalism also a shadowing correction for the higher Fock component of the
photon containing gluons. The corresponding magnitudes of gluon shadowing
correction are compared adopting different phenomenological dipole models. Our
results are tested by available data from the E665 and NMC collaborations.
Finally, the magnitude of nuclear shadowing is predicted for various kinematic
regions that should be scanned by the future experiments at electron-ion
colliders.
