Wakamatsu-silting complexes

TL;DR

This paper introduces Wakamatsu-silting complexes, a new class generalizing silting and Wakamatsu-tilting modules, providing characterizations and exploring their properties and conjectures related to finitistic dimension.

Contribution

It defines Wakamatsu-silting complexes, establishes their properties, and connects their conjectured classification to the finitistic dimension conjecture.

Findings

Wakamatsu-silting complexes generalize silting and Wakamatsu-tilting modules.

A complex is Wakamatsu-silting if and only if its dual is Wakamatsu-silting.

The conjecture that all compact Wakamatsu-silting complexes are silting is linked to the finitistic dimension conjecture.

Abstract

We introduce Wakamatsu-silting complexes (resp., Wakamatsu-tilting complexes) as a common generalization of both silting complexes (resp., tilting complexes) and Wakamatsu-tilting modules. Characterizations of Wakamatsu-silting complexes are given. In particular, we show that a complex $T$ is Wakamatsu-silting if and only if its dual $DT$ is Wakamatsu-silting. It is conjectured that all compact Wakamatsu-silting complexes are just silting complexes. We prove that the conjecture lies under the finitistic dimension conjecture.