A note on the Segal conjecture for large objects
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909133857357824 |
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| author | Burklund, Robert Subramanian, Vignesh |
| author_facet | Burklund, Robert Subramanian, Vignesh |
| contents | The Segal conjecture for $C_p$ (as proved by Lin and Gunawardena) asserts that the canonical map from the $p$-complete sphere spectrum to the Tate construction for the trivial action of $C_p$ on the $p$-complete sphere spectrum is an isomorphism. In this article we extend the collection of spectra for which the canonical map $X \to X^{tC_p}$ is known to be an isomorphism to include any $p$-complete, bounded below spectrum whose mod $p$ homology, viewed a module over the Steenrod algebra, is complete with respect to the maximal ideal $I \subseteq \mathcal{A}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the Segal conjecture for large objects Burklund, Robert Subramanian, Vignesh Algebraic Topology The Segal conjecture for $C_p$ (as proved by Lin and Gunawardena) asserts that the canonical map from the $p$-complete sphere spectrum to the Tate construction for the trivial action of $C_p$ on the $p$-complete sphere spectrum is an isomorphism. In this article we extend the collection of spectra for which the canonical map $X \to X^{tC_p}$ is known to be an isomorphism to include any $p$-complete, bounded below spectrum whose mod $p$ homology, viewed a module over the Steenrod algebra, is complete with respect to the maximal ideal $I \subseteq \mathcal{A}$. |
| title | A note on the Segal conjecture for large objects |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2403.06724 |