Tilting theory for extended module categories
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910776765186048 |
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| author | Zhou, Yu |
| author_facet | Zhou, Yu |
| contents | 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 $τ_{[m]}$-tilting pairs and show bijections between $τ_{[m]}$-tilting pairs, $(m+1)$-term silting complexes, and functorially finite $s$-torsion pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15473 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tilting theory for extended module categories Zhou, Yu Representation Theory Category Theory Rings and Algebras 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 $τ_{[m]}$-tilting pairs and show bijections between $τ_{[m]}$-tilting pairs, $(m+1)$-term silting complexes, and functorially finite $s$-torsion pairs. |
| title | Tilting theory for extended module categories |
| topic | Representation Theory Category Theory Rings and Algebras |
| url | https://arxiv.org/abs/2411.15473 |