We report on low temperature magneto-conductance measurements of a single modulation-doped GaAs/AlGaAs core-shell nanowire in transverse magnetic field. Information on the phase coherence length l(phi) is obtained from quantum conductivity corrections due to weak localization effects or universal conductance fluctuation. The nanowires are totally coherent at very low temperature and l(phi) could be larger than 250 nm at 4 K. The temperature dependence of l(phi) shows that the main dephasing mechanism is the one-dimensional electron-electron scattering mechanism. (c) 2013 Elsevier B.V. All rights reserved.