Fishing for complements

Angeleri Hugel, Lidia and Pauksztello, David and Vitoria, Jorge (2025) Fishing for complements. Nagoya Mathematical Journal. ISSN 0027-7630

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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.