Silting objects

TL;DR

This paper surveys recent advances in silting theory, exploring its connections with t-structures, co-t-structures, and classification results in derived categories, highlighting new insights into silting and cosilting objects.

Contribution

It provides a comprehensive overview of silting theory, comparing different notions and their interplay with other structures, and presents classification results in specific algebraic contexts.

Findings

Comparison of silting notions and their relations with t-structures

Classification results for silting objects over commutative noetherian rings

Analysis of silting-discrete algebras

Abstract

We give an overview of recent developments in silting theory. After an introduction on torsion pairs in triangulated categories, we discuss and compare different notions of silting and explain the interplay with t-structures and co-t-structures. We then focus on silting and cosilting objects in a triangulated category with coproducts and study the case of the unbounded derived category of a ring. We close the survey with some classification results over commutative noetherian rings and silting-discrete algebras.