Timeline for When do the polynomial algebra and free algebra coincide in brave new algebra?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 28, 2017 at 11:35 | history | edited | AAK | CC BY-SA 3.0 |
incorporate observation from comments
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| Apr 28, 2017 at 11:25 | comment | added | AAK | Ah, good point. That simplifies the proof a bit as well, thanks! | |
| Apr 28, 2017 at 5:01 | comment | added | A Rock and a Hard Place | I do think that should be the case: if $\pi_0R$ is a $\mathbb Q$-algebra, then all $\pi_nR$ are rational vector spaces, so $R$ is $\mathbb Q$-local. Since rationalization is a smashing equivalence and $L_\mathbb QS\simeq \mathbb Q,$ then $R\simeq L_\mathbb QR\simeq \mathbb Q\otimes R$ which is clearly an $\mathbb E_\infty$-$\mathbb Q$-algebra. | |
| Apr 28, 2017 at 0:29 | comment | added | A Rock and a Hard Place | Wonderful, thank you very much! Does $\pi_0R$ being a $\mathbb Q$-algebra suffice for $R$ (maybe connective?) to be a $\mathbb Q$-algebra, as an $\mathbb E_\infty$-ring? Is that something that has to do with the motto: "the rational sphere is the rational Eilenberg-MacLane"? | |
| Apr 28, 2017 at 0:11 | vote | accept | A Rock and a Hard Place | ||
| Apr 27, 2017 at 23:13 | history | answered | AAK | CC BY-SA 3.0 |