Measurements of the centrality and rapidity dependence of inclusive jet production in s NN= 5.02 TeV proton–lead (p+ Pb) collisions and the jet cross-section in s= 2.76 TeV proton–proton collisions are presented. These quantities are measured in datasets corresponding to an integrated luminosity of 27.8 nb− 1 and 4.0 pb− 1, respectively, recorded with the ATLAS detector at the Large Hadron Collider in 2013. The p+ Pb collision centrality was characterised using the total transverse energy measured in the pseudorapidity interval− 4.9< η<− 3.2 in the direction of the lead beam. Results are presented for the double-differential per-collision yields as a function of jet rapidity and transverse momentum (p T) for minimum-bias and centrality-selected p+ Pb collisions, and are compared to the jet rate from the geometric expectation. The total jet yield in minimum-bias events is slightly enhanced above the expectation in a …