  Charmonium is a prominent probe of the Quark-Gluon Plasma (QGP), expected to
be formed in ultrarelativistic heavy-ion (A-A) collisions. It has been
predicted that the J/psi(c-cbar) particle is dissolved in the deconfined medium
created in A-A systems. However this suppression can be counterbalanced via
regeneration of the charm/anti-charm bound state in QGP or via statistical
production at the phase boundary. At LHC energies, the latter mechanisms are
expected to play a more important role, due to a charm production cross section
significantly larger than at lower energies.
  Measurements obtained by the ALICE experiment for inclusive J/psi production
are shown, making use of Pb-Pb data at sqrt(s_NN) = 2.76 TeV, collected in 2010
and 2011. In particular, the focus is given on the nuclear modification factor,
R_AA, derived for forward (2.5 < y < 4) and mid rapidities (|y| < 0.9), both
down to zero transverse momentum (pT). The centrality, y and pT dependences of
R_AA are presented and discussed in the context of theoretical models, together
with PHENIX and CMS results.
