Homological stratification and descent
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914406433030144 |
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| author | Barthel, Tobias Heard, Drew Sanders, Beren Zou, Changhan |
| author_facet | Barthel, Tobias Heard, Drew Sanders, Beren Zou, Changhan |
| contents | We introduce a notion of stratification for rigidly-compactly generated tensor-triangulated categories relative to the homological spectrum and develop the fundamental features of this theory. In particular, we demonstrate that it exhibits excellent descent properties. In conjunction with Balmer's Nerves of Steel conjecture, we conclude that stratification admits a general form of descent. This gives a uniform treatment of several recent stratification results and provides a complete answer to the question: When does stratification descend? As a new application, we extend earlier work on the tensor triangular geometry of equivariant module spectra from finite groups to compact Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13956 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homological stratification and descent Barthel, Tobias Heard, Drew Sanders, Beren Zou, Changhan Category Theory Algebraic Topology Representation Theory 18F99, 18G65, 18G80, 20C10, 55P91, 55U35 We introduce a notion of stratification for rigidly-compactly generated tensor-triangulated categories relative to the homological spectrum and develop the fundamental features of this theory. In particular, we demonstrate that it exhibits excellent descent properties. In conjunction with Balmer's Nerves of Steel conjecture, we conclude that stratification admits a general form of descent. This gives a uniform treatment of several recent stratification results and provides a complete answer to the question: When does stratification descend? As a new application, we extend earlier work on the tensor triangular geometry of equivariant module spectra from finite groups to compact Lie groups. |
| title | Homological stratification and descent |
| topic | Category Theory Algebraic Topology Representation Theory 18F99, 18G65, 18G80, 20C10, 55P91, 55U35 |
| url | https://arxiv.org/abs/2412.13956 |