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I am a postdoc in maths with a degree in theoretical physics. I am interested in mathematical structures in quantum field theory and string theory, see here.

1d
comment Nonunital $E_\infty$-rings
Ah, right. Excellent, thanks!
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reviewed Approve suggested edit on abstract-polytopes tag wiki
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asked Nonunital $E_\infty$-rings
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comment Power operations and Lambda-structure-like lifts of Frobenius in $E_\infty$-geometry?
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
19
accepted AdicCompletion$\dashv$Torsion adjunction on spectra?
Aug
18
comment Power operations and Lambda-structure-like lifts of Frobenius in $E_\infty$-geometry?
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
18
comment Power operations and Lambda-structure-like lifts of Frobenius in $E_\infty$-geometry?
Thanks! You mean Strickland 98 (ncatlab.org/nlab/show/power+operation#Strickland98). Also, you seem to think of some established theory of Frobenius lifts in this case, maybe you could provide further pointers to the literature for that?
Aug
16
awarded  Inquisitive
Aug
15
comment Power operations and Lambda-structure-like lifts of Frobenius in $E_\infty$-geometry?
This is excellent, thank you. I have taken the liberty of recording a version of your reply here: ncatlab.org/nlab/show/power+operation#OnK1LocalKUAlgebras
Aug
15
revised Power operations and Lambda-structure-like lifts of Frobenius in $E_\infty$-geometry?
added 28 characters in body; edited title
Aug
15
asked Power operations and Lambda-structure-like lifts of Frobenius in $E_\infty$-geometry?
Aug
14
revised Construction of the Lie functor: left vs. right invariant vector fields on Lie groups and Lie groupoids
fixed trivial typo
Aug
13
reviewed Approve suggested edit on average number of cycles and closed walks length k in incomplete directed graph
Aug
13
reviewed Approve suggested edit on Matching number and chromatic number
Aug
12
reviewed Reject suggested edit on nontrivial theorems with trivial proofs
Aug
12
comment AdicCompletion$\dashv$Torsion adjunction on spectra?
Thanks! I had missed that. This is excellent, just what I was hoping for. Thanks again.
Aug
12
comment AdicCompletion$\dashv$Torsion adjunction on spectra?
Secondly, just to sanity check: so then for every smashing localization there is in fact canonically a pair of fracture squares which -- when regarded in the opposite $\mathrm{Spectra}^{\mathrm{op}}$ -- fit into an exact hexagon of just the "differential cohomology hexagon"-form discussed here: ncatlab.org/nlab/show/… -- where $\flat$ is the given localization and $\Pi$ the given co-localization.
Aug
12
comment AdicCompletion$\dashv$Torsion adjunction on spectra?
Thank you, Charles, this is very much appreciated. Please allow me to follow up with two more questions, which will be no less trivial than the previous ones must have been: First: so will the functors of p-completion and p-torsion approximation as functors from spectra to spectra not be both left and right adjoint to each other?
Aug
12
comment AdicCompletion$\dashv$Torsion adjunction on spectra?
Second question, related to that: is there an issue with variance here? maybe I am mixed up, sorry. In what you write p-torsion approximation is left adjoint, but in that story of "Greenlees-May duality" on the level of chain complexes it is right adjoint, no? Do we have a dual statement?
Aug
12
comment AdicCompletion$\dashv$Torsion adjunction on spectra?
Thanks, Charles. I am behind the curve here, please bear with me. I realize that the statement you refer to is prop. 2.5 in Bousfield 79. Two questions, though, I still have: First regarding "holds for any smashing localization": for what I am after I suppose I'd have to read that as "holds whenever one of the two localizations is smashing and the other's acyclification is the 'co-smashing' co-localization of the former"?