The subgroup stratification of Nakaoka spectra
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912535757717504 |
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| author | Wisdom, Noah |
| author_facet | Wisdom, Noah |
| contents | We construct a stratification on the Nakaoka spectrum of any $G$-Tambara functor indexed by the poset of subgroups of $G$. When $G$ is Dedekind, we show that the $H$th stratum of the Nakaoka spectrum of the Burnside $G$-Tambara functor is closed and not open; this provides examples of étale maps which induce closed, non-open maps on Nakaoka spectra. By computing the strata on the ghost of a $C_p$-Tambara functor we obtain many examples of étale maps of Tambara functors for which the induced map on Nakaoka spectra is not open, in contrast to the non-equivariant world. We also compute the strata of all fixed-point Tambara functors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The subgroup stratification of Nakaoka spectra Wisdom, Noah Algebraic Topology Algebraic Geometry We construct a stratification on the Nakaoka spectrum of any $G$-Tambara functor indexed by the poset of subgroups of $G$. When $G$ is Dedekind, we show that the $H$th stratum of the Nakaoka spectrum of the Burnside $G$-Tambara functor is closed and not open; this provides examples of étale maps which induce closed, non-open maps on Nakaoka spectra. By computing the strata on the ghost of a $C_p$-Tambara functor we obtain many examples of étale maps of Tambara functors for which the induced map on Nakaoka spectra is not open, in contrast to the non-equivariant world. We also compute the strata of all fixed-point Tambara functors. |
| title | The subgroup stratification of Nakaoka spectra |
| topic | Algebraic Topology Algebraic Geometry |
| url | https://arxiv.org/abs/2508.09360 |