Derived Equivalences Between Associative Deformations

TL;DR

This paper proves that derived Morita equivalence between associative deformations over the same complete local ring implies classical Morita equivalence, establishing a significant link between these two notions.

Contribution

It demonstrates that derived Morita equivalence coincides with Morita equivalence for associative deformations over complete local rings, clarifying their relationship.

Findings

Derived Morita equivalence implies Morita equivalence for associative deformations.

Establishes a condition under which derived and classical equivalences coincide.

Provides a new understanding of the structure of associative deformations.

Abstract

We prove that if two associative deformations (parameterized by the same complete local ring) are derived Morita equivalent, then they are Morita equivalent (in the classical sense).