The p(T)-differential production cross sections of the prompt charmed
mesons D-0, D+, D*(-), and D-s(+) and their charge conjugate in the
rapidity interval -0.96 < y(cms) < 0.04 were measured in p-Pb collisions
at a center-of-mass energy root s(NN) = 5.02 TeV with the ALICE detector
at the LHC. The nuclear modification factor R-pPb, quantifying the
D-meson yield in p-Pb collisions relative to the yield in pp collisions
scaled by the number of binary nucleon-nucleon collisions, is compatible
within the 15%-20% uncertainties with unity in the transverse momentum
interval 1 < p(T) < 24 GeV/c. No significant difference among the R-pPb
of the four D-meson species is observed. The results are described
within uncertainties by theoretical calculations that include
initial-state effects. The measurement adds experimental evidence that
the modification of the momentum spectrum of D mesons observed in Pb-Pb
collisions with respect to pp collisions is due to strong final-state
effects induced by hot partonic matter