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

2026/04/10 by Noah Wisdom · 2 voices
Mathematics · #math.KT

paper · pdf

Abstract

In previous work, the author and Chan computed the algebraic K-theory of the constant C₂-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_pⁿ-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.

Citations

• Determining unit groups and K₁ of finite rings
• Trace methods for equivariant algebraic K-theory
• Clarification and Coinduction of Tambara Functors
• A classification of C_pⁿ-Tambara fields
• Nemo/Hecke: Computer Algebra and Number Theory Packages for the Julia Programming Language
• Ideals of Tambara functors
• On the non-existence of elements of Kervaire invariant one
• On the nonexistence of elements of Kervaire invariant one

Discussions

• Noah Wisdom The $K$-theory of finite Tambara fields: away from $p$ https://arxiv.org/abs/2604.09954 [bsky, 0 points, 0 comments]
• Noah Wisdom: The $K$-theory of finite Tambara fields: away from $p$ https://arxiv.org/abs/2604.09954 https://arxiv.org/pdf/2604.09954 https://arxiv.org/html/2604.09954 [bsky, 0 points, 0 comments]

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