  Measurements of the centrality and rapidity dependence of inclusive jet
production in $\sqrt{s_\mathrm{NN}} = 5.02$ TeV proton--lead ($p$+Pb)
collisions and the jet cross-section in $\sqrt{s} = 2.76$ 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 $-4.9 < \eta < -3.2$
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 ($p_\mathrm{T}$) 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 $p_\mathrm{T}$-dependent manner but is consistent
with the expectation within uncertainties. The ratios of jet spectra from
different centrality selections show a strong modification of jet production at
all $p_\mathrm{T}$ at forward rapidities and for large $p_\mathrm{T}$ at
mid-rapidity, which manifests as a suppression of the jet yield in central
events and an enhancement in peripheral events. These effects imply that the
factorisation between hard and soft processes is violated at an unexpected
level in proton-nucleus collisions. Furthermore, the modifications at forward
rapidities are found to be a function of the total jet energy only, implying
that the violations may have a simple dependence on the hard parton-parton
kinematics.
