Simples in a cotilting heart

TL;DR

This paper characterizes simple objects and their injective envelopes in the hearts of t-structures induced by cotilting modules over rings, integrating torsion theory, model theory, and Auslander-Reiten theory.

Contribution

It provides a detailed description of simple objects in the Grothendieck hearts associated with cotilting modules, combining multiple theoretical frameworks.

Findings

Identifies simple objects in the heart of the t-structure

Determines injective envelopes of these simple objects

Links torsion theory with model theory and Auslander-Reiten theory

Abstract

Every cotilting module over a ring R induces a t-structure with a Grothendieck heart in the derived category D(Mod R). We determine the simple objects in this heart and their injective envelopes, combining torsion-theoretic aspects with methods from the model theory of modules and Auslander-Reiten theory.