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arXiv · 2604.09954

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

Noah Wisdom
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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.

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Noah Wisdom. 2026-04-10. The $K$-theory of finite Tambara fields: away from $p$. https://arxiv.org/abs/2604.09954

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