Quarkonium production in p-Pb collisions with ALICE

ALICE has measured quarkonium production in p-Pb collisions at backward ($-$4.46 $<$ $y_{\rm cms}$ $<$ $-$2.96), mid ($-$1.37 $<$ $y_{\rm cms}$ $<$ 0.43) and forward (2.03 $<$ $y_{\rm cms}$ $<$ 3.53) rapidity ($y$) regions down to zero transverse momentum ($p_{\rm T}$). The inclusive J/$\psi$ production has been studied at mid-$y$ in p-Pb interactions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV and at forward and backward $y$ in p-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV and 8.16 TeV. The comparison of the J/$\psi$ production to the one of the loosely bound $\psi$(2S) state is discussed, together with new results on the nuclear modification factors of the $\Upsilon$(1S) and $\Upsilon$(2S) states measured at forward and backward $y$. All the results will be compared to those obtained at lower energies and with available theoretical calculations.