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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2604.09954 |
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| _version_ | 1866915932109012992 |
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| author | Wisdom, Noah |
| author_facet | Wisdom, Noah |
| contents | In previous work, the author and 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09954 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The $K$-theory of finite Tambara fields: away from $p$ Wisdom, Noah K-Theory and Homology 19D50 (primary), 19A49, 55P91 (secondary) In previous work, the author and 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. |
| title | The $K$-theory of finite Tambara fields: away from $p$ |
| topic | K-Theory and Homology 19D50 (primary), 19A49, 55P91 (secondary) |
| url | https://arxiv.org/abs/2604.09954 |