« first day (1819 days earlier)      last day (1584 days later) » 

Praphulla Koushik
Praphulla Koushik
1:11 PM
 
Saal Hardali
Saal Hardali
1:31 PM
is there any evidence whatsover that the number n in in morava K(n) (i.e the chromatic height) is related the number n in $\infty-n$ categories?
 
Peter Nelson
Peter Nelson
why would you think that it is
 
Tim Campion
Tim Campion
I mean, that's supposed to be the idea behind the redshift conjecture, since algebraic K-theory is supposed to increase the n in infinity n categories. But I'm curious about this too. I don't know any real evidence.
 
Peter Nelson
Peter Nelson
i mean i guess there's also the stolz-teichner stuff
 
Saal Hardali
Saal Hardali
Apart from redshift conjectures there's the stolze teichner thing
yeah, exactly.
I'm wondering whether there's more evidence of the numerical sort for this.
 
Tim Campion
Tim Campion
If you look at TAF stuff, is there any hint of higher categories going on?
Oh, numerical evidence
 
Saal Hardali
Saal Hardali
1:37 PM
I mean chromatic redshift counts as sort of numerical evidence i'd say.
 
Tim Campion
Tim Campion
There exist people looking seriously for this kind of thing, but I forget how.
 
 
1 hour later…
user351585
2:44 PM
@skd Sure, let me see if I can get them done this week
 
user351585
3:01 PM
@TimCampion Some work on relationships between v_n-periodic homology and higher-categorical models for topological field theories seems to have been done by somebody named Schommer-Pries ;) mediathek.uni-regensburg.de/playthis/5976eb2e3e30c9.54286370
 
Tim Campion
Tim Campion
3:29 PM
@aaaaaaaaaaaaaaa lol, and good point!
Super-naive question. If I have a 1-dimensional commutative formal group $\mathbb G$, can I take some kind of Jacobian variety of $\mathbb G$? And if $\mathbb G$ has height $n$, will the dimension of the Jacobian be $n$?
 
user351585
3:52 PM
The classical thing works sort of the reverse of what you wrote: a smooth projective curve of genus g has a Jacobian, which is a g-dim'l abelian variety; and the p-div'l group of a g-dim'l abelian variety (over a separably closed field, let's say) will be dimension g, height 2g, and satisfy Serre duality, so you can write down all the possible 1-dim'l summands in it by an easy method
 

« first day (1819 days earlier)      last day (1584 days later) »