Universal deformation rings and derived equivalences

TL;DR

This paper demonstrates that certain derived and stable functors preserve the isomorphism classes of versal deformation rings of Gorenstein-projective modules over finite dimensional algebras, extending existing results in the field.

Contribution

It generalizes Velázquez-Marulanda's result to singular equivalences of Morita type with levels and shows stable equivalences of Morita type also preserve these deformation rings.

Findings

Stable functors of derived equivalences preserve deformation ring isomorphism classes.

Generalization of Velázquez-Marulanda's result to singular equivalences of Morita type.

Stable equivalences of Morita type preserve deformation ring isomorphism classes.

Abstract

In this paper, we show that stable functors of derived equivalences preserve the isomorphism classes of versal deformation rings of finitely generated Gorenstein-projective modules over finite dimensional $k$-algebras. Then we generalize Vel\'ez-Marulanda's result \cite{V} in the case of singular equivalences of Morita type with levels for Gorenstein algebras. Moreover, we also prove that stable equivalences of Morita type preserve the isomorphism classes of versal deformation rings of finitely generated Gorenstein-projective modules over finite dimensional $k$-algebras.