The spectrum of the Burnside Tambara functor
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915760149889024 |
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| author | Calle, Maxine Elena Chan, David Mehrle, David Quigley, J. D. Spitz, Ben Van Niel, Danika |
| author_facet | Calle, Maxine Elena Chan, David Mehrle, David Quigley, J. D. Spitz, Ben Van Niel, Danika |
| contents | We compute the spectrum of prime ideals in the Burnside Tambara functor over an arbitrary finite group. Our proof uses recent advances in the commutative algebra of Tambara functors, as well as a Tambara functor analogue of ghost coordinates which works over arbitrary finite groups and clarifies some previous computations. As examples, we explicitly compute the spectrum of the Burnside Tambara functor over all dihederal groups, the quaternion group $Q_8$, the alternating group $A_4$, and the general linear group $GL_3(F_2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10727 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The spectrum of the Burnside Tambara functor Calle, Maxine Elena Chan, David Mehrle, David Quigley, J. D. Spitz, Ben Van Niel, Danika Algebraic Topology Commutative Algebra Group Theory 19A22 (Primary), 55P91, 13A15 We compute the spectrum of prime ideals in the Burnside Tambara functor over an arbitrary finite group. Our proof uses recent advances in the commutative algebra of Tambara functors, as well as a Tambara functor analogue of ghost coordinates which works over arbitrary finite groups and clarifies some previous computations. As examples, we explicitly compute the spectrum of the Burnside Tambara functor over all dihederal groups, the quaternion group $Q_8$, the alternating group $A_4$, and the general linear group $GL_3(F_2)$. |
| title | The spectrum of the Burnside Tambara functor |
| topic | Algebraic Topology Commutative Algebra Group Theory 19A22 (Primary), 55P91, 13A15 |
| url | https://arxiv.org/abs/2506.10727 |