The Residue Theorem via an Explicit Construction of Traces

Let be a locally Noetherian scheme and φ: → be a morphism of finite type, whose fibers have bounded dimensions. Given a residual complex • on with Cousin data, a residual complex φ! • on with Cousin data has been constructed. In this article, transitivity of residual complexes is clarified and a trace map tr / : φ*φ! • → • is constructed in terms of Cousin data. With these concrete data, the residue theorem is directly proved.