  In the energy range of RHIC and LHC the mechanisms of nuclear suppression of
charmonia are expected to be strikingly different from what is known for the
energy of the SPS. One cannot think any more of charmonium produced on a bound
nucleon which then attenuates as it passes through the rest of the nucleus. The
coherence length of charmonium production substantially exceeds the nuclear
radius in the new energy range. Therefore the production amplitudes on
different nucleons, rather than the cross sections, add up and interfere, i.e.
shadowing is at work. So far no theoretical tool has been available to
calculate nuclear effects for charmonium production in this energy regime. We
develop a light-cone Green function formalism which incorporates the effects of
the coherence of the production amplitudes and of charmonium wave function
formation, and is the central result of this paper. We found a substantial
deviation from QCD factorization, namely, gluon shadowing is much stronger for
charmonium production than it is in DIS. We predict for nuclear effects $x_2$
scaling which is violated at lower energies by initial state energy loss which
must be also included in order to compare with available data. In this paper
only the indirect J/Psi originating from decay of P-wave charmonia are
considered. The calculated x_F-dependence of J/Psi nuclear suppression is in a
good accord with data. We predict a dramatic variation of nuclear suppression
with x_F in pA and a peculiar peak at x_F=0 in AA collisions at RHIC.
