Fishing for complements

2024/02/20 by Hügel, Lidia Angeleri, Pauksztello, David, Vitória, Jorge
#16G10 #18G05 #18G80 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2402.13356

Abstract

Given a presilting object in a triangulated category, we find necessary and sufficient conditions for the existence of a complement. This is done both for classic (pre)silting objects and for large (pre)silting objects. The key technique is the study of associated co-t-structures. As a consequence of our techniques we recover some known cases of the existence of complements, including for derived categories of some hereditary abelian categories and for silting-discrete algebras. Moreover, we also show that a finite-dimensional algebra is silting discrete if and only if every bounded large silting complex is equivalent to a compact one.

Related

• Silting Theory in triangulated categories with coproducts
• On a characterization of (co)silting objects
• A negative answer to Complement Question for presilting complexes
• Silting reduction and Calabi--Yau reduction of triangulated categories
• When is the silting-discreteness inherited?