  We generalize the leading twist theory of nuclear shadowing and calculate
quark and gluon generalized parton distributions (GPDs) of spinless nuclei. We
predict very large nuclear shadowing for nuclear GPDs. In the limit of the
purely transverse momentum transfer, our nuclear GPDs become
impact-parameter-dependent nuclear parton distributions (PDFs). Nuclear
shadowing induces nontrivial correlations between the impact parameter b and
the light-cone fraction x. We make predictions for the deeply virtual Compton
scattering (DVCS) amplitude and the DVCS cross section on Pb-208 at high
energies. We calculate the cross section of the Bethe-Heitler (BH) process and
address the issue of the extraction of the DVCS signal from the e A \to e
\gamma A cross section. We find that the e A \to e \gamma A differential cross
section is dominated by DVCS at the momentum transfer t near the minima of the
nuclear form factor. We also find that nuclear shadowing leads to dramatic
oscillations of the DVCS beam-spin asymmetry, A_{LU}, as a function of t. The
position of the points where A_{LU} changes sign is directly related to the
magnitude of nuclear shadowing.
