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arXiv · 2512.13218

AIR tilting subcategories of extended hearts

Jiaqun Wei·Yu Zhou
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Abstract

We introduce the notion of AIR tilting subcategories of extended hearts of $t$-structures on a triangulated category associated with silting subcategories. This notion generalizes $\tau_{[d]}$-tilting pairs of extended finitely generated modules over finite-dimensional algebras to a more general framework, which includes both extended large modules over unitary rings and truncated subcategories of finite-dimensional derived categories of proper non-positive differential graded algebras. Within this setting, we establish a bijection between AIR tilting subcategories and silting subcategories. Furthermore, we define quasi-tilting and tilting subcategories of extended hearts, extending the corresponding notions from module categories, and investigate their fundamental properties along with the relationships among these tilting-related classes.

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BibTeXRIS

Jiaqun Wei, Yu Zhou. 2025-12-15. AIR tilting subcategories of extended hearts. https://arxiv.org/abs/2512.13218

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