Equivalences induced by infinitely generated tilting modules

TL;DR

This paper extends classical theorems on module category equivalences to infinitely generated tilting modules over arbitrary rings, broadening the scope of tilting theory in algebra.

Contribution

It generalizes Brenner-Butler and Happel's theorems to infinitely generated tilting modules over arbitrary rings, establishing new equivalences in module and derived categories.

Findings

Established equivalences between subcategories of module categories.

Extended tilting theory to infinitely generated modules.

Connected module and derived category equivalences.

Abstract

We generalize Brenner and Butler's Theorem as well as Happel's Theorem on the equivalences induced by a finitely generated tilting module over artin algebras, to the case of an infinitely generated tilting module over an arbitrary associative ring establishing the equivalences induced between subcategories of module categories and also at the level of derived categories.