Patch-density in tensor-triangular geometry
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917961784098816 |
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| author | Balmer, Paul Gallauer, Martin |
| author_facet | Balmer, Paul Gallauer, Martin |
| contents | The spectrum of a tensor-triangulated category carries a compact Hausdorff topology, called the constructible topology, also known as the patch topology. We prove that patch-dense subsets detect tt-ideals and we prove that any infinite family of tt-functors that detects nilpotence provides such a patch-dense subset. We review several applications and examples in algebra, in topology and in the representation theory of profinite groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15274 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Patch-density in tensor-triangular geometry Balmer, Paul Gallauer, Martin Category Theory Algebraic Topology Representation Theory The spectrum of a tensor-triangulated category carries a compact Hausdorff topology, called the constructible topology, also known as the patch topology. We prove that patch-dense subsets detect tt-ideals and we prove that any infinite family of tt-functors that detects nilpotence provides such a patch-dense subset. We review several applications and examples in algebra, in topology and in the representation theory of profinite groups. |
| title | Patch-density in tensor-triangular geometry |
| topic | Category Theory Algebraic Topology Representation Theory |
| url | https://arxiv.org/abs/2503.15274 |