Tilting Modules over Almost Perfect Domains

TL;DR

This paper classifies all tilting modules and classes over almost perfect domains, extending known classifications from Dedekind and 1-Gorenstein domains, and also classifies cotilting modules in the Noetherian case.

Contribution

It provides a comprehensive classification of tilting and cotilting modules over almost perfect domains, generalizing previous results for specific domain types.

Findings

Complete classification of tilting modules over almost perfect domains

Classification of tilting classes over these domains

Cotilting modules classified in the Noetherian case

Abstract

We provide a complete classification of all tilting modules and tilting classes over almost perfect domains, which generalizes the classifications of tilting modules and tilting classes over Dedekind and 1-Gorenstein domains. Assuming the APD is Noetherian, a complete classification of all cotilting modules is obtained (as duals of the tilting ones).