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The fact that the conserved current of a gauge symmetry is reduced to a superpotential is proved in a very general setting. In contrast with gauge symmetries, nontrivial Noether identities of Lagrangian field theory are well described in homology terms     . Therefore, we define nontrivial gauge symmetries as those associated to complete nontrivial Noether identities in accordance with the second Noether theorem (Theorem 5). Given a nontrivial gauge symmetry of a Lagrangian L, thedoi:10.1142/s0219887809003862 fatcat:cw7nuh6pb5dgdj3x3m2qmf4h5m