Inverting Integers in Tambara Functors
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912844966002688 |
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| author | Spitz, Ben |
| author_facet | Spitz, Ben |
| contents | Let $G$ be a finite group, and $k$ an integer. In this note, we show that for any $G$-Tambara functor $T$ and any subgroups $H_1, H_2 \leq G$, $k$ is a unit in $T(G/H_1)$ if and only if $k$ is a unit in $T(G/H_2)$. In other words, one may speak unambiguously of the localization $T[1/k]$. As a consequence, the norm functors $N_H^G$ commute with inverting $k$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_25891 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverting Integers in Tambara Functors Spitz, Ben Group Theory Algebraic Topology Representation Theory 13A50, 13B30 (Primary), 55P91, 55Q91 (Secondary) Let $G$ be a finite group, and $k$ an integer. In this note, we show that for any $G$-Tambara functor $T$ and any subgroups $H_1, H_2 \leq G$, $k$ is a unit in $T(G/H_1)$ if and only if $k$ is a unit in $T(G/H_2)$. In other words, one may speak unambiguously of the localization $T[1/k]$. As a consequence, the norm functors $N_H^G$ commute with inverting $k$. |
| title | Inverting Integers in Tambara Functors |
| topic | Group Theory Algebraic Topology Representation Theory 13A50, 13B30 (Primary), 55P91, 55Q91 (Secondary) |
| url | https://arxiv.org/abs/2510.25891 |