Algebraically Closed Fields in Equivariant Algebra

2025/05/08 by Jason Schuchardt, Schuchardt, Jason, Ben Spitz +3 · 3 citations
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2505.05539

openalex publication_date 2025/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the Burklund-Schlank-Yuan abstraction of ``algebraically closed" to ``Nullstellensatzian", we show that a G-Tambara functor is Nullstellensatzian if and only if it is the coinduction of an algebraically closed field (for any finite group G). As a consequence we deduce an equivalence between the K-theory spectrum of any Nullstellensatzian G-Tambara functor with the K theory of some algebraically closed field.

Cited by

• Inverting Integers in Tambara Functors
• The algebraic K-theory of Green functors
• Clarification and Coinduction of Tambara Functors

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