Recollements for dualizing $k$-varieties and Auslander's formulas
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2017
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| _version_ | 1866912385615265792 |
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| author | Ogawa, Yasuaki |
| author_facet | Ogawa, Yasuaki |
| contents | Given the pair of a dualizing $k$-variety and its functorially finite subcategory, we show that there exists a recollement consisting of their functor categories of finitely presented objects. We provide several applications for Auslander's formulas: The first one realizes a module category as a Serre quotient of a suitable functor category. The second one shows a close connection between Auslander-Bridger sequences and recollements. The third one gives a new proof of the higher defect formula which includes the higher Auslander-Reiten duality as a special case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1703_06224 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Recollements for dualizing $k$-varieties and Auslander's formulas Ogawa, Yasuaki Category Theory Representation Theory Given the pair of a dualizing $k$-variety and its functorially finite subcategory, we show that there exists a recollement consisting of their functor categories of finitely presented objects. We provide several applications for Auslander's formulas: The first one realizes a module category as a Serre quotient of a suitable functor category. The second one shows a close connection between Auslander-Bridger sequences and recollements. The third one gives a new proof of the higher defect formula which includes the higher Auslander-Reiten duality as a special case. |
| title | Recollements for dualizing $k$-varieties and Auslander's formulas |
| topic | Category Theory Representation Theory |
| url | https://arxiv.org/abs/1703.06224 |