Detecting derived equivalences with the CHZ criterion
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914449800036352 |
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| author | Pavon, Sergio |
| author_facet | Pavon, Sergio |
| contents | In 2018, Chen, Han and Zhou introduced a criterion to determine whether the HRS-tilt at a given torsion pair induces derived equivalence. We showcase four applications of this criterion: to stable torsion pairs in arbitrary abelian categories (which we prove to always induce derived equivalence), to abelian categories of global dimension at most two, to (co)hereditary torsion pairs over artin algebras (for which we give a purely combinatorial criterion for derived equivalence), and to study whether irreducible silting mutation acts transitively on two-term tilting complexes over a finite dimensional algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Detecting derived equivalences with the CHZ criterion Pavon, Sergio Representation Theory Commutative Algebra Category Theory 18E40, 18G80, 16S90, 13D30 In 2018, Chen, Han and Zhou introduced a criterion to determine whether the HRS-tilt at a given torsion pair induces derived equivalence. We showcase four applications of this criterion: to stable torsion pairs in arbitrary abelian categories (which we prove to always induce derived equivalence), to abelian categories of global dimension at most two, to (co)hereditary torsion pairs over artin algebras (for which we give a purely combinatorial criterion for derived equivalence), and to study whether irreducible silting mutation acts transitively on two-term tilting complexes over a finite dimensional algebra. |
| title | Detecting derived equivalences with the CHZ criterion |
| topic | Representation Theory Commutative Algebra Category Theory 18E40, 18G80, 16S90, 13D30 |
| url | https://arxiv.org/abs/2509.12983 |