From observations collected with the ESPaDOnS spectropolarimeter, we report the discovery of magnetic fields at the surface of the mildly accreting classical T Tauri star V2129 Oph. Zeeman signatures are detected, both in photospheric lines and in the emission lines formed at the base of the accretion funnels linking the disc to the protostar, and monitored over the whole rotation cycle of V2129 Oph. We observe that rotational modulation dominates the temporal variations of both unpolarized and circularly polarized line profiles. We reconstruct the large-scale magnetic topology at the surface of V2129 Oph from both sets of Zeeman signatures simultaneously. We find it to be rather complex, with a dominant octupolar component and a weak dipole of strengths 1.2 and 0.35 kG, respectively, both slightly tilted with respect to the rotation axis. The large-scale field is anchored in a pair of 2-kG unipolar radial field spots located at high latitudes and coinciding with cool dark polar spots at photospheric level. This large-scale field geometry is unusually complex compared to those of non-accreting cool active subgiants with moderate rotation rates. As an illustration, we provide a first attempt at modelling the magnetospheric topology and accretion funnels of V2129 Oph using field extrapolation. We find that the magnetosphere of V2129 Oph must extend to about 7R* to ensure that the footpoints of accretion funnels coincide with the high-latitude accretion spots on the stellar surface. It suggests that the stellar magnetic field succeeds in coupling to the accretion disc as far out as the corotation radius, and could possibly explain the slow rotation of V2129 Oph. The magnetospheric geometry we derive produces X-ray coronal fluxes typical of those observed in cTTSs.
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