Silting t-structures in $Q$-shaped derived categories

Mathematics > Representation Theory [Submitted on 18 Jun 2026] Title:Silting t-structures in $Q$-shaped derived categories View PDF HTML (experimental)Abstract:Torsion pairs, and in particular t-structures, play a central role in the study of triangulated categories. Specifically, t-structures induced by silting (or tilting) objects often admit desirable properties with strong connections to derived equivalences. In this paper, using the correspondence of Saorín-Šťovíček between cohereditary cotorsion pairs in Frobenius exact categories and t-structures in their stable categories, we construct a family of t-structures in the $Q$-shaped derived category of Holm and Jorgensen, arising from admissible partitions of $Q$. We give an explicit description of the associated cotorsion pairs inside the Frobenius exact category of the bifibrant objects, and we identify the corresponding co-aisles by certain homological vanishing conditions. Such t-structures are proved to be induced by a silting object, that can be completely determined by the combinatorics of $Q$. Finally, we illustrate our results by recovering well-known equivalences in the $Q$-shaped setting, while also providing examples where the combinatorial conditions fail (e.g. cyclic quivers), showing that such categories may admit no non-trivial t-structures, revealing phenomena analogous to those observed by Linckelmann in stable module categories. Submission history From: Anastasios Slaftsos [view email][v1] Thu, 18 Jun 2026 16:24:58 UTC (120 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.