Algebraically Closed Fields in Equivariant Algebra
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913827931553792 |
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| author | Schuchardt, Jason Spitz, Ben Wisdom, Noah |
| author_facet | Schuchardt, Jason Spitz, Ben Wisdom, Noah |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05539 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraically Closed Fields in Equivariant Algebra Schuchardt, Jason Spitz, Ben Wisdom, Noah Algebraic Topology Commutative Algebra K-Theory and Homology 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. |
| title | Algebraically Closed Fields in Equivariant Algebra |
| topic | Algebraic Topology Commutative Algebra K-Theory and Homology |
| url | https://arxiv.org/abs/2505.05539 |