The formal spectrum of a tensor-triangulated category
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910031492939776 |
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| author | Heard, Drew Nielsen, Marius |
| author_facet | Heard, Drew Nielsen, Marius |
| contents | To any essentially small tensor-triangulated category $\mathcal{K}$ and Thomason subset $Y \subseteq \mathrm{Spc}(\mathcal{K})$ we associate a ringed space $(\mathrm{Spf}(\mathcal{K},Y), \mathcal{O}_{\mathrm{Spf}(\mathcal{K},Y)}),$ called the formal spectrum of $(\mathcal{K},Y)$. We establish basic properties of this construction and compute it in several examples from algebraic geometry, chromatic homotopy theory, equivariant homotopy theory, and modular representation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20835 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The formal spectrum of a tensor-triangulated category Heard, Drew Nielsen, Marius Algebraic Topology Algebraic Geometry Category Theory To any essentially small tensor-triangulated category $\mathcal{K}$ and Thomason subset $Y \subseteq \mathrm{Spc}(\mathcal{K})$ we associate a ringed space $(\mathrm{Spf}(\mathcal{K},Y), \mathcal{O}_{\mathrm{Spf}(\mathcal{K},Y)}),$ called the formal spectrum of $(\mathcal{K},Y)$. We establish basic properties of this construction and compute it in several examples from algebraic geometry, chromatic homotopy theory, equivariant homotopy theory, and modular representation theory. |
| title | The formal spectrum of a tensor-triangulated category |
| topic | Algebraic Topology Algebraic Geometry Category Theory |
| url | https://arxiv.org/abs/2602.20835 |