Topology and the axial anomaly in abelian lattice gauge theories

The axial anomaly in abelian lattice gauge theories is shown to be equal to a simple quadratic expression in the gauge field tensor plus a removable divergence term if the lattice Dirac operator satisfies the Ginsparg-Wilson relation. The theorem is a consequence of the locality, the gauge invariance and the topological nature of the anomaly and does not refer to any other properties of the lattice theory.