Local equivalence via homological algebra

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.

There is an irrecoverable error in Lemma 2.5. There are counterexamples even in case R=Q[x]. The lemma is crucial for the rest of the paper and it does not work unless strong assumptions are made (like: the modules are graded)