Timeline for The “field of fractions” of the sphere spectrum (localization at $\pi_0(\mathbb{S})\setminus\{0\}$, the non-zero integers)
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 5, 2023 at 1:35 | comment | added | David White | It is worth pointing out that this localization far predates Lurie's Higher Algebra. You can find it (that is, localizing a spectrum at a subset of homotopy elements) in writings of Bousfield from the 1970s, and Adams even earlier. | |
| Mar 31, 2023 at 22:16 | vote | accept | Emily | ||
| Mar 31, 2023 at 17:59 | answer | added | Tyler Lawson | timeline score: 7 | |
| Mar 31, 2023 at 16:31 | history | edited | Emily | CC BY-SA 4.0 |
edited title
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| Mar 31, 2023 at 16:24 | history | edited | Emily | CC BY-SA 4.0 |
added 94 characters in body
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| Mar 31, 2023 at 16:24 | comment | added | Emily | @Z.M I'm not sure about the precise form of $(\pi_0(\mathbb{S})\setminus\{0\})^{-1}\mathbb{S}$, but I think we should be fine since we are inverting only the nonzero elements in $\pi_0(\mathbb{S})$, which are all non-torsion. HA 7.2.3.19 and 7.2.3.20 seem relevant here; e.g. I wonder if we have elements like $[\nu]/k$ in $\pi_1((\pi_0(\mathbb{S})\setminus)\mathbb{S})$. | |
| Mar 31, 2023 at 6:28 | comment | added | Z. M | I am not sure whether I am mistaken, but the first localization seems to be simply $\mathbb Q$, since higher homotopy groups of the sphere are finite. | |
| Mar 30, 2023 at 23:42 | history | asked | Emily | CC BY-SA 4.0 |