Timeline for Power operations and Lambda-structure-like lifts of Frobenius in $E_\infty$-geometry?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 21, 2014 at 10:00 | comment | added | Urs Schreiber | As David Corfield kindly points out to me elsewhere: explicit comments/speculation on relation between power operations and Borger-style absolute geometry is in Morava-Santhanam 12 (ncatlab.org/nlab/show/power+operation#MoravaSanthanam12) referring to closely related discussion in Guillot 06 (ncatlab.org/nlab/show/power+operation#Guillot06) | |
| Aug 18, 2014 at 9:58 | comment | added | Urs Schreiber | Thanks, Charles! I was hoping you would see this, despite being busy at ICM. Below in the comments to Akhil Mathew's answer it seems that Elden Elmanto is thinking of some general concept of Frobenius lifts for at least some class of $E_\infty$-rings. (?) The story of $\Lambda$-rings in view of $\mathbb{F}_1$ suggests that what matters for having a Frobenius-like endomorphism is not characteristic $p$ as such, but reduction to a maximal ideal. From this analogy I would expect $E_\infty$-analogs of Frobenius at each prime for $K(n)$-local spectra. Any chance for that? | |
| Aug 17, 2014 at 7:27 | comment | added | Charles Rezk | It's not really clear what it means to "lift Frobenius" in the setting of $E_\infty$-rings, because it is not clear what "Frobenius" means. There are relatively few $E_\infty$-rings which are "characterstic $p$" (those that exist must have underlying spectra which are products of Eilenberg-Mac Lane spectra). Further, there is no natural Frobenius endomorphism on the class of char $p$ $E_\infty$-ring spectra. | |
| Aug 15, 2014 at 17:19 | answer | added | Akhil Mathew | timeline score: 9 | |
| Aug 15, 2014 at 14:39 | history | edited | Urs Schreiber | CC BY-SA 3.0 |
added 28 characters in body; edited title
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| Aug 15, 2014 at 14:24 | history | asked | Urs Schreiber | CC BY-SA 3.0 |