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 d ivergence term if the lattice Dirac operator satisfies the Ginsparg-Wilson relation. The theorem is a consequence of the locality, the gauge invarianc e and the topological nature of the anomaly and does not refer to any other properties of the lattice theory, (C) 1999 Elsevier Science B.V.