Profinite transfers in chromatic homotopy theory and analogs of J

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• Guchuan Li (Peking University)
• Thursday 19 June 2025, 11:45-12:45
• Seminar Room 1, Newton Institute.

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EHTW04 - Beyond the telescope conjecture

After $K(1)$-localization, Adams’s image of $J$ can be regarded 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 $\Sigma}{-1} KO_2^{\wedge \to L{K(1)} S}0$. We define transfer maps generally as duals to restriction maps. For arbitrary heights $n$ and closed subgroups $G \subset \mathbb{G}_n$ in the Morava stabilizer group, these transfer maps give analogs of the classical $J$ homomorphism at higher chromatic heights. This is joint work in progress with Ningchuan Zhang.

This talk is part of the Isaac Newton Institute Seminar Series series.

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