Local equivalence via homological algebra

TL;DR

This paper explores local equivalence of bounded complexes over polynomial rings using homological algebra, providing a unified approach to existing results in the literature.

Contribution

It introduces a homological algebra framework to analyze local equivalence of complexes over polynomial rings, unifying various prior results.

Findings

Homological algebra approach to local equivalence

Unified proof framework for existing results

Applicability to complexes over polynomial rings

Abstract

We study local equivalence of bounded complexes over a polynomial ring $R[w]$, where $R$ is a noetherian ring. We provide a homological algebra approach to the results, the variants of which have been proved in many places in the literature.