The $\mathbb{Z}/p$-equivariant spectrum $BP\mathbb{R}$ for an odd prime $p$
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909265544871936 |
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| author | Hu, Po Kriz, Igor Somberg, Petr Zou, Foling |
| author_facet | Hu, Po Kriz, Igor Somberg, Petr Zou, Foling |
| contents | In the present paper, we construct a $\mathbb{Z}/p$-equivariant analog of the $\mathbb{Z}/2$-equivariant spectrum $BP\mathbb{R}$ previously constructed by Hu and Kriz. We prove that this spectrum has some of the properties conjectured by Hill, Hopkins, and Ravenel. Our main construction method is an $\mathbb{Z}/p$-equivariant analog of the Brown-Peterson tower of $BP$, based on a previous description of the $\mathbb{Z}/p$-equivariant Steenrod algebra with constant coefficients by the authors. We also describe several variants of our construction and comparisons with other known equivariant spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16599 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $\mathbb{Z}/p$-equivariant spectrum $BP\mathbb{R}$ for an odd prime $p$ Hu, Po Kriz, Igor Somberg, Petr Zou, Foling Algebraic Topology 55P42, 55P91, 55P92 In the present paper, we construct a $\mathbb{Z}/p$-equivariant analog of the $\mathbb{Z}/2$-equivariant spectrum $BP\mathbb{R}$ previously constructed by Hu and Kriz. We prove that this spectrum has some of the properties conjectured by Hill, Hopkins, and Ravenel. Our main construction method is an $\mathbb{Z}/p$-equivariant analog of the Brown-Peterson tower of $BP$, based on a previous description of the $\mathbb{Z}/p$-equivariant Steenrod algebra with constant coefficients by the authors. We also describe several variants of our construction and comparisons with other known equivariant spectra. |
| title | The $\mathbb{Z}/p$-equivariant spectrum $BP\mathbb{R}$ for an odd prime $p$ |
| topic | Algebraic Topology 55P42, 55P91, 55P92 |
| url | https://arxiv.org/abs/2407.16599 |