The importance of being isolated
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911698288377856 |
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| author | Balchin, Scott Gómez, Juan Omar Stevenson, Greg |
| author_facet | Balchin, Scott Gómez, Juan Omar Stevenson, Greg |
| contents | We give both a sufficient condition for and an obstruction to the derived category of a commutative ring being generated by its residue fields. As an illustration, we exhibit a ring for which Foxby's small support classifies localizing subcategories despite the failure of the local-to-global principle. We also conclude that the residue fields do not generate for a polynomial ring in infinitely many variables. Finally, we give a necessary and sufficient criterion for the derived category to satisfy the local-to-global principle; it turns out to depend solely on the topology of the spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19617 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The importance of being isolated Balchin, Scott Gómez, Juan Omar Stevenson, Greg Commutative Algebra Category Theory We give both a sufficient condition for and an obstruction to the derived category of a commutative ring being generated by its residue fields. As an illustration, we exhibit a ring for which Foxby's small support classifies localizing subcategories despite the failure of the local-to-global principle. We also conclude that the residue fields do not generate for a polynomial ring in infinitely many variables. Finally, we give a necessary and sufficient criterion for the derived category to satisfy the local-to-global principle; it turns out to depend solely on the topology of the spectrum. |
| title | The importance of being isolated |
| topic | Commutative Algebra Category Theory |
| url | https://arxiv.org/abs/2605.19617 |