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Apr 27 at 4:55 history edited Eric Peterson CC BY-SA 4.0
edited body
Sep 2, 2021 at 3:49 vote accept kiran
Sep 2, 2021 at 1:08 comment added Eric Peterson Irakli also comments: these kinds of counterexamples are not possible in $R$-modules where $R_*$ is of global dimension 1, as a universal coefficient spectral sequence can be used to decompose modules into sums of quotients by homotopy elements. This rules out the possibility of similar examples using $KU$ or $ku/p$ in place of $ku$. Bearing this in mind, $ku$ is among the simplest ring spectra with larger homotopy global dimension, so it makes sense to begin a search here.
Sep 1, 2021 at 21:12 history edited Eric Peterson CC BY-SA 4.0
once more be careful about what \beta denotes
Sep 1, 2021 at 20:55 comment added Eric Peterson Intentional: a bare $\mathbb F_2$ is a graded abelian group concentrated in degree $0$, and $\Sigma^n \mathbb F_2$ is a graded abelian group concentrated in degree $n$, whereas $H \mathbb F_2$ is a spectrum.
Sep 1, 2021 at 19:31 comment added მამუკა ჯიბლაძე Are $\Sigma^*\mathbb F_2$ instead of $\Sigma^*H\mathbb F_2$ intentional or just a typo?
Sep 1, 2021 at 19:18 history edited Eric Peterson CC BY-SA 4.0
no, really, use beta to mean one thing
Sep 1, 2021 at 18:45 history edited Eric Peterson CC BY-SA 4.0
don't use beta to mean two things
Sep 1, 2021 at 18:37 history answered Eric Peterson CC BY-SA 4.0