The $K$-theory of finite Tambara fields: away from $p$

[2604.09954] The $K$-theory of finite Tambara fields: away from $p$ Skip to main content Search Submit Donate Log in Mathematics > K-Theory and Homology arXiv:2604.09954 (math) [Submitted on 10 Apr 2026 ( v1 ), last revised 26 Aug 2026 (this version, v2)] Title: The $K$-theory of finite Tambara fields: away from $p$ Authors: Noah Wisdom View PDF HTML (experimental) Abstract: In previous work, the author and David Chan computed the algebraic $K$-theory of the constant $C_2$-Tambara field with value the field with two elements, using a method which fails at odd primes. Herein we make progress towards the corresponding odd primary computations using a completely new idea. Particularly, we show that the $K$-theory groups of any constant $C_{p^n}$-Tambara field with value a characteristic $p$ finite field are torsion, and we completely determine these groups after inverting $p$. The away-from-$p$-torsion satisfies a simple pattern predicted by previous work, and a computer-aided computation shows that the $p$-power torsion is nontrivial in general. Comments: 8 pages, added a section with the relevant Julia commands to establish the claimed computation of K_1 in the last section. Comments welcome! Subjects: K-Theory and Homology (math.KT) MSC classes: 19D50 (primary), 19A49, 55P91 (secondary) Cite as: arXiv:2604.09954 [math.KT] (or arXiv:2604.09954v2 [math.KT] for this version) https://doi.org/10.48550/arXiv.2604.09954 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Noah Wisdom [ view email ] [v1] Fri, 10 Apr 2026 23:24:11 UTC (20 KB) [v2] Wed, 26 Aug 2026 21:22:30 UTC (21 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.KT < prev | next > new | recent | 2026-04 Change to browse by: math 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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