A residue calculus approach to the uniform Artin-Rees lemma

TL;DR

This paper presents a new analytic proof of the uniform Artin-Rees lemma using residue calculus, introducing a novel product of complexes of vector bundles with potential applications in division problems.

Contribution

It provides the first analytic proof of the uniform Artin-Rees lemma and introduces a new product of complexes of vector bundles for division problems.

Findings

Analytic proof of the uniform Artin-Rees lemma.

Introduction of a new product of complexes of vector bundles.

Potential applications in division problems with product ideals.

Abstract

The uniform Artin-Rees lemma has been proved by C. Huneke using algebraic methods. We give a new proof for this result in the analytic setting using residue calculus. We also have to introduce a type of product of complexes of vector bundles, which may be applicable in the solution of other division problems with respect to product ideals.