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11:08 AM
Are perfect rings (of char p) Thom spectra?
The Moore spectrum of W(k) seems to have a commutative ring structure
Replace by this ring spectrum the p-adic sphere
 
 
9 hours later…
skd
8:04 PM
@FrankScience not sure if this is what you're looking for, but here's a possible solution. let k be a perfect F_p-algebra, and let S_{W(k)} denote the spherical witt vectors. this is an E_oo-ring which is flat over the (p-complete) sphere spectrum S, and pi_0(S_{W(k)}) = W(k). consider the map L^2 S^3 -> BGL_1(S_{W(k)}) classifying the element 1+p in pi_0 GL_1(S_{W(k)}); the thom spectrum is the free E_2-S_{W(k)}-algebra F with a nullhomotopy of p.
by general formal properties, this is the same as the base-change to S_{W(k)} of the free E_2-algebra with a nullhomotopy of p, which by hopkins-mahowald is the base-change to S_{W(k)} of HF_p. Since S_{W(k)} is flat over S, this is just isomorphic to Hk, so k is a thom spectrum over S_{W(k)}
 
 
2 hours later…
9:40 PM
Anyone know what the K(n)-nilpotent completion of E_n is?
@skd what are the spherical Witt vectors?
 
10:38 PM
@JonathanBeardsley re sphereical Witt vectors: Example 5.2.7 of Elliptic II
and re E_n: should just be E_n back again I would think, unless I don't know what "nilpotent completion" means
 

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