The homological spectrum via definable subcategories
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916560013099008 |
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| author | Bird, Isaac Williamson, Jordan |
| author_facet | Bird, Isaac Williamson, Jordan |
| contents | We develop an alternative approach to the homological spectrum of a tensor-triangulated category through the lens of definable subcategories. This culminates in a proof that the homological spectrum is homeomorphic to a quotient of the Ziegler spectrum. Along the way, we characterise injective objects in homological residue fields in terms of the definable subcategory corresponding to a given homological prime. We use these results to give a purity perspective on the relationship between the homological and Balmer spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_05179 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The homological spectrum via definable subcategories Bird, Isaac Williamson, Jordan Category Theory Algebraic Topology Representation Theory 18G80, 18F99, 18E45, 18E10 We develop an alternative approach to the homological spectrum of a tensor-triangulated category through the lens of definable subcategories. This culminates in a proof that the homological spectrum is homeomorphic to a quotient of the Ziegler spectrum. Along the way, we characterise injective objects in homological residue fields in terms of the definable subcategory corresponding to a given homological prime. We use these results to give a purity perspective on the relationship between the homological and Balmer spectrum. |
| title | The homological spectrum via definable subcategories |
| topic | Category Theory Algebraic Topology Representation Theory 18G80, 18F99, 18E45, 18E10 |
| url | https://arxiv.org/abs/2304.05179 |