We give multiplicity based criteria for integral dependence of modules. This type of criteria goes back to Rees, who treated the case of zero-dimensional ideals in local rings. Much later, Flenner and Manaresi were able to extend Rees's work to arbitrary ideals, using the notion of j-multiplicity instead of the classical Hilbert-Samuel multiplicity. We consider the general case of arbitrary finitely generated modules. Our proof is self-contained and relatively short, and implies the earlier algebraic results as special cases.

This is a report on joint work with Javid Validashti.

Lecture #13405

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