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arXiv · 2411.15473

Tilting theory for extended module categories

Yu Zhou
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Abstract

In extended hearts of bounded $t$-structures on a triangulated category, we provide a Happel-Reiten-Smalo tilting theorem and a characterization for $s$-torsion pairs. Applying these to $m$-extended module categories, we characterize torsion pairs induced by $(m+1)$-term silting complexes. After establishing Auslander-Reiten theory in extended module categories, we introduce $\tau_{[m]}$-tilting pairs and show bijections between $\tau_{[m]}$-tilting pairs, $(m+1)$-term silting complexes, and functorially finite $s$-torsion pairs.

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Yu Zhou. 2024-11-23. Tilting theory for extended module categories. https://arxiv.org/abs/2411.15473

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