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SUMMARY:Profinite transfers in chromatic homotopy theory and analogs of J 
 - Guchuan Li (Peking University)
DTSTART:20250619T104500Z
DTEND:20250619T114500Z
UID:TALK232936@talks.cam.ac.uk
DESCRIPTION:After $K(1)$-localization\, Adams's image of $J$ can be regard
 ed as a transfer map: specifically\, the transfer from the $C_2$-homotopy 
 fixed points to the $\\mathbb{Z}2^\\times$-homotopy fixed points for $E_1$
 . This map corresponds to the canonical morphism $\\Sigma^{-1} KO_2^\\wedg
 e \\to L{K(1)} S^0$. We define transfer maps generally as duals to restric
 tion maps. For arbitrary heights $n$ and closed subgroups $G \\subset \\ma
 thbb{G}_n$ in the Morava stabilizer group\, these transfer maps give analo
 gs of the classical $J$ homomorphism at higher chromatic heights. This is 
 joint work in progress with Ningchuan Zhang.
LOCATION:Seminar Room 1\, Newton Institute
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