Timeline for Is $KU\otimes S^1_+$ isomorphic to $F(S^1_+,KU)$ as $E_\infty$ rings?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 15, 2023 at 3:38 | vote | accept | Neil Strickland | ||
| Nov 13, 2023 at 7:24 | comment | added | Maxime Ramzi | Your answer looks perfectly fine :) | |
| Nov 12, 2023 at 20:17 | comment | added | Neil Strickland | @MaximeRamzi I think that you are right. I have entered my own answer along those lines, but if you prefer to enter your own answer, then I will accept it. | |
| Nov 12, 2023 at 20:15 | answer | added | Neil Strickland | timeline score: 8 | |
| Nov 12, 2023 at 19:51 | comment | added | Maxime Ramzi | Oh, right, shouldn't that answer the question completely ? Namely the equivalence of KU-modules between the two is classified by the Bott element, and this lifts to a strct element by ""Snaith", so the equivalence lifts to an E_oo-equivalence ? | |
| Nov 12, 2023 at 19:47 | comment | added | Maxime Ramzi | Snaith's theorem implies that the Bott element is a strict element, right ? I mean it's much more elementary than Snaith I guess, it's essentially the inclusion from Picard into the semiring of finite dimensional C-vector spaces (topologized). | |
| Nov 12, 2023 at 19:08 | comment | added | Neil Strickland | @MaximeRamzi Yes, I think my question is at least closely related to the question of whether the Bott element is a strict unit in $KU$. I guess you are referring to Theorem H of "The chromatic nullstellensatz" which implies that the strict unit spectrum of a suitable algebraic extension of $KU^\wedge_p$ is $\Sigma^2\mathbb{Z}_p\oplus\overline{\mathbb{F}_p}^\times$. The question is whether there is a corresponding $\Sigma^2\mathbb{Z}$ in the strict unit spectrum of $KU$ itself. | |
| Nov 12, 2023 at 18:42 | comment | added | Maxime Ramzi | The computation of strict units of E in the Nullstellensatz paper also suggests that there is some interesting commutative algebra map $KU[S^1] \to KU^{S^1}$, at least up to p-completion and going to $KU^{nr}$ | |
| Nov 12, 2023 at 15:36 | comment | added | Shay Ben Moshe | A small remark is that the $p$-adic case is at least somewhat related to the chromatic Fourier transform, as in Hopkins-Lurie Ambidexterity Corollary 5.3.26 or Barthel-Carmeli-Schlank-Yanovski Theorem A/Theorem D. I didn't think this through and don't see immediately how to connect them. | |
| Nov 12, 2023 at 14:45 | history | asked | Neil Strickland | CC BY-SA 4.0 |