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Jonathan Beardsley
Jonathan Beardsley
00:06
omfg i am just crushing on some category theory today...
enriched grothendieck construction is no joke
 
2 hours later…
Arun Debray
Arun Debray
02:07
Someone told me today that, just as spectrally enriched Mackey functors model G-spectra, spectrally enriched Tambara functors should model G-ring spectra, but that this is hard to make precise.
Is there a reference for this model of G-ring spectra? Or is this more of a heuristic?
 
10 hours later…
Dylan Wilson
Dylan Wilson
11:49
It depends what you mean. What did you have in mind for the trivial group, for example?
Denis Nardin
Denis Nardin
12:44
@ArunDebray There is a way to make it formal for connective G-commutative rings (that is, by considering Tambara functors in spaces). As far as I know there's no such description for general things though
The space version should be in Rolf Hoyer's thesis
 
1 hour later…
Arun Debray
Arun Debray
14:05
@DylanWilson good point. The notion of a Tambara functor for G = * is still something nontrivial, and I can work what that is.
@DenisNardin thanks! I'll go check it out.
 
2 hours later…
Sean Tilson
Sean Tilson
15:44
Anyone have an electronic version that is complete of Kochman's book on Bordism and the adams SS?
 
4 hours later…
Tyler Lawson
Tyler Lawson
19:20
@skd geometrically you're looking a map Spec(Z) -> M_{fg} classifying the additive formal group law. as stated, that map isn't flat so the Landweber exact functor theorem doesn't produce a (co)homology theory for you out of it (I don't think integral homology is a functor of MU_*-homology).
one construction of KO comes from a map BC_2 -> M_{fg} which is flat. it doesn't look flat on global sections, but locally it's flat
said another way, KO comes from building KU (which is flat) with a C_2-action. (though Landweber's theorem, and the Hopkins-Miller theorem, aren't actually strong enough to do this)
Joe Berner
Joe Berner
has anyone systematically worked on "profinite completion away from p" for spaces? This idea goes back to Artin-Mazur, but it hasn't been updated into model categorical or infinity categorical language.
Tyler Lawson
Tyler Lawson
i think most people would speculate that there's no sheaf of spectra on M_{fgl} (in some hideous topology) whose sections over Spec(Z) is HZ; but I don't know that there are any theorems along that line, particularly because the definition of "hideous topology" is up for grabs
 
2 hours later…
Charles Rezk
Charles Rezk
21:22
In SAG (9.3.1.8) there's a notion of the "derived moduli stack of formal groups". It is defined as a functor of points, which sidesteps the problem of the characterizing the Hideous Topology.
Sean Tilson
Sean Tilson
22:04
So I think a lot of the djvu's are cut off in dropbox, is this dropbox doing this?

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