Timeline for Thom Spectra and Hopf-Galois Extensions of Ring Spectra
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 24, 2016 at 16:32 | vote | accept | Jonathan Beardsley | ||
| Feb 24, 2016 at 16:32 | answer | added | Jonathan Beardsley | timeline score: 1 | |
| Dec 1, 2014 at 0:48 | history | edited | Jonathan Beardsley | CC BY-SA 3.0 |
fixed a minor error in notation
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| Nov 14, 2014 at 14:11 | comment | added | Jonathan Beardsley | I should perhaps also add that in certain nice cases I have been able to work this out (the write-ups are on my website). But that relies on the collapse of a certain Kunneth spectral sequence which seems unlikely in general. It would be nice to have more general conditions. | |
| May 30, 2014 at 14:57 | comment | added | Jonathan Beardsley | I should also mention that that convergence I mention definitely holds for a LOT of interesting Thom spectra: $MU$, $MSO$, $MSU$, $X(n)$, Baker and Richter's $M\xi$. And the alternate situation (being an extension of the 2-adic sphere spectrum) holds for $MO$. | |
| May 30, 2014 at 14:07 | comment | added | Jonathan Beardsley | Ah thanks @JustinNoel I had seen that word (primitives) used in some places. Perhaps it will be less confusing if I start using that rather than cofixed points. | |
| May 30, 2014 at 11:53 | comment | added | Justin Noel | I would like to point out that $Mf$ being $\mathbb{Z}$-orientable is not a very severe restriction and follows from $G$ being simply connected. The condition is equivalent to $f$ lifting to the simply connected cover $BSL_1 S$ of $BGL_1 S$. Assuming your Hopf-Galois condition is essentially the convergence of the associated Adams spectral sequence, when $Mf$ is not $\mathbb{Z}$-orientable then you obtain a Hopf-Galois extension of the 2-adic sphere spectrum. Also in the algebraic context of coactions, what you are calling cofixed points are traditionally called primitives. | |
| May 30, 2014 at 0:47 | history | edited | Jonathan Beardsley |
edited tags
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| May 30, 2014 at 0:29 | history | asked | Jonathan Beardsley | CC BY-SA 3.0 |