We give a new proof of a recent result due to Mats Andersson and Elizabeth Wulcan, generalizing the local Grothendieck duality theorem. It can also be seen as a generalization of a previous result by Mikael Passare. Our method does not require the use of the Hironaka desingularization theorem and it provides a semi-explicit realization of the residue that is annihilated by functions from the given ideal.
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