A negative answer to Complement Question for presilting complexes

TL;DR

This paper demonstrates, using a geometric model, that some presilting complexes over finite-dimensional algebras are not summands of silting complexes, providing a negative answer to the complement question.

Contribution

It introduces a geometric approach to show the existence of presilting complexes that are not summands of silting complexes, addressing a key open question.

Findings

Existence of presilting complexes not summands of silting complexes

Geometric model used to analyze presilting complexes

Negative answer to the complement question in this context

Abstract

In this paper using a geometric model we show that there is a presilting complex over a finite dimensional algebra, which is not a direct summand of a silting complex.