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ABSTRACT It has recently been demonstrated that self-consistent particle-in-cell simulations of low-obliquity pulsar magnetospheres in flat spacetime show weak particle acceleration and no pair production near the poles. We investigate the validity of this conclusion in a more realistic spacetime geometry via general-relativistic particle-in-cell simulations of the aligned pulsar magnetosphere with pair formation. We find that the addition of the frame-dragging effect makes the local current density along the magnetic field larger than the Goldreich-Julian value, which leads to unscreened parallel electric fields and the ignition of a pair cascade. When pair production is active, we observe field oscillations in the open field bundle, which could be related to pulsar radio emission. We conclude that general-relativistic effects are essential for the existence of the pulsar mechanism in low-obliquity rotators.