Timeline for Homotopy groups of homotopy fixed points of a $\mathbb{Z}\left[\frac{1}{\lvert G\rvert}\right]$-local orthogonal spectrum
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| May 8, 2022 at 16:35 | comment | added | Urs | Thanks, yes you are right, I mean $G$ and corrected it. | |
| May 8, 2022 at 16:17 | history | edited | Urs | CC BY-SA 4.0 |
deleted 1 character in body
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| May 8, 2022 at 15:17 | comment | added | user164898 | Maybe there is some subtlety I have missed (for example, I am assuming that by $BK$ you mean $G$), but the classical Bousfield-Kan spectral sequence of the form $H^*(G; \pi_*(X)) \Rightarrow \pi_*(X^{hG})$ is natural in the choice of group $G$. By Maschke's theorem, your localness hypothesis is enough to ensure that $H^*(G; \pi_*(X))$ agrees with $H^*(1; \pi_*(X))$, so the map from the BKSS for the $G$-action on $X$ to the action of the trivial group on $X$ is an isomorphism on $E_2$-terms. So it's an isomorphism on $E_{\infty}$-terms, so $\pi_*(X^{hG}) \rightarrow \pi_*(X)$ is an isomorphism. | |
| May 8, 2022 at 14:28 | history | edited | Urs | CC BY-SA 4.0 |
added 44 characters in body; edited title
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| S May 8, 2022 at 13:50 | review | First questions | |||
| May 8, 2022 at 17:29 | |||||
| S May 8, 2022 at 13:50 | history | asked | Urs | CC BY-SA 4.0 |