Timeline for Cohomology theory with only one Adams operation?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Dec 11, 2019 at 1:47 | vote | accept | John Greenwood | ||
| Dec 9, 2019 at 17:26 | comment | added | John Greenwood | @DenisNardin thanks for the link, it looks like $E$-theory is the thing to learn about! | |
| Dec 8, 2019 at 18:21 | answer | added | Neil Strickland | timeline score: 5 | |
| Dec 8, 2019 at 7:48 | comment | added | S. carmeli | @TimCampion The notion of $\delta$ ring you refer to is only a "semi-$\delta$-ring". Unfortunately, it does not satisfy in general the multiplicative axiom. In fact, what is the right generalization of $\delta$-ring that is satisfied by the ambidextruous $\delta$-operation and its analogues is still unclear at all, at least to us. Moreover, the main feature used is not the one you mensioned but the fact that there's a unique such structure on $\mathbb{Z}_p$, and it reduces the valuation of every number by exactly $1$ if it is not invertible. | |
| S Dec 7, 2019 at 17:06 | history | suggested | Igor Sikora |
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| Dec 7, 2019 at 11:13 | review | Suggested edits | |||
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| Dec 7, 2019 at 7:14 | comment | added | Denis Nardin | Not quite what you're asking for, but $\delta$-rings appear very naturally via the power operations on $p$-completed $E$-theory, where they're called $\theta$-rings. Arguably this is a better analogy, since you'd expect the Frobenius to be a map of rings, not a map of modules (as cohomology operations are). | |
| Dec 7, 2019 at 0:19 | comment | added | Tim Campion | You're probably right, I really am not as familiar with Adams operations as I should be. Btw in the paper I linked to, the $\delta$-ring stuff first gets going at the beginning of Section 4 (at least I'm guessing it's the same meaning of "$\delta$-ring"). As I understand it, the key property they end up using is that in a $\delta$-ring, all torsion is nilpotent. It's referred to in the abstract as "a certain power operation". | |
| Dec 7, 2019 at 0:16 | comment | added | John Greenwood | @TimCampion I don't think so, because Adams operations at invertible primes are easy to construct. Thanks for the reference, I will have a look! | |
| Dec 7, 2019 at 0:06 | comment | added | Tim Campion | I think $p$-completed $K$-theory should fit the bill. For an interesting application of $\delta$-rings in stable homotopy theory, see here. | |
| Dec 6, 2019 at 23:33 | history | edited | John Greenwood | CC BY-SA 4.0 |
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| Dec 6, 2019 at 23:10 | history | asked | John Greenwood | CC BY-SA 4.0 |