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In the gauge-invariant construction of abelian chiral gaug e theories on the lattice based on the Ginsparg-Wilson relation, the gauge anomaly is topologica l and its cohomologically trivial part plays the role of the local counter term. We give a prescripti on o solve the local cohomology problem within a finite lattice by reformulating the Poincar é lemma so that it holds true on the finite lattice up to exponentially small corrections. Moreo v r we perform a caluculation of the trivial part of the anomaly numerically, which is given by th e solution of the local cohomology problem.

A practical construction of U(1) chiral lattice gauge theories