The subgroup stratification of Nakaoka spectra

[2508.09360] The subgroup stratification of Nakaoka spectra Skip to main content Search Submit Donate Log in Mathematics > Algebraic Topology arXiv:2508.09360 (math) [Submitted on 12 Aug 2025 ( v1 ), last revised 26 Aug 2026 (this version, v2)] Title: The subgroup stratification of Nakaoka spectra Authors: Noah Wisdom View PDF HTML (experimental) Abstract: 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. Comments: 15 pages with a new figure, comments welcome! Final revision incorporating referee comments Subjects: Algebraic Topology (math.AT) ; Algebraic Geometry (math.AG) Cite as: arXiv:2508.09360 [math.AT] (or arXiv:2508.09360v2 [math.AT] for this version) https://doi.org/10.48550/arXiv.2508.09360 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Noah Wisdom [ view email ] [v1] Tue, 12 Aug 2025 21:42:52 UTC (35 KB) [v2] Wed, 26 Aug 2026 22:19:38 UTC (49 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AT < prev | next > new | recent | 2025-08 Change to browse by: math math.AG References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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