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Inclusive ϒ(1S) and ϒ(2S) production have been measured in Pb–Pb collisions at the centre-of-mass energy per nucleon–nucleon pair √sNN = 5.02 TeV, using the ALICE detector at the CERN LHC. The ϒ mesons are reconstructed in the centre-of-mass rapidity interval 2.5 < y < 4 and in the transversemomentum range pT < 15 GeV/c, via their decays to muon pairs. In this Letter, we present results on the inclusive ϒ(1S) nuclear modification factor RAA as a function of collision centrality, transverse momentum and rapidity. The ϒ(1S) and ϒ(2S) RAA, integrated over the centrality range 0–90%, are 0.37± 0.02(stat) ± 0.03(syst) and 0.10 ± 0.04(stat) ± 0.02(syst), respectively, leading to a ratio Rϒ(2S) AA /Rϒ(1S) AA of 0.28±0.12(stat)±0.06(syst). The observed ϒ(1S) suppression increases with the centrality of the collision and no significant variation is observed as a function of transverse momentum and rapidity.