Silting modules over commutative rings

TL;DR

This paper extends the classification of tilting modules over commutative rings by introducing silting modules, which correspond to all Gabriel topologies of finite type, not just faithful ones.

Contribution

It generalizes the existing classification by replacing tilting modules with silting modules, removing the faithfulness restriction.

Findings

Silting modules correspond to all Gabriel topologies of finite type.

The classification of modules over commutative rings is expanded.

The relationship between silting modules and Gabriel topologies is established.

Abstract

Tilting modules over commutative rings were recently classified in [12]: they correspond bijectively to faithful Gabriel topologies of finite type. In this note we extend this classification by dropping faithfulness. The counterpart of an arbitrary Gabriel topology of finite type is obtained by replacing tilting with the more general notion of a silting module.