Transchromatic phenomena in the equivariant slice spectral sequence

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• XiaoLin Danny Shi (University of Washington)
• Monday 12 June 2023, 11:45-12:45
• Seminar Room 1, Newton Institute.

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HHHW06 - HHH follow on: Homotopy: fruit of the fertile furrow

In this talk, we will construct a stratification for the equivariant slice spectral sequence. This stratification is achieved through the localized slice spectral sequences, which compute the geometric fixed points equipped with residual quotient group actions.  As an application, we will utilize this stratification to investigate norms of Real bordism theories and their quotients. These quotients hold significant importance in Hill—Hopkins—Ravenel’s resolution of the Kervaire invariant one problem, as well as in the study of fixed points of Lubin—Tate theories by finite subgroups of the Morava stabilizer group. For these theories, the stratification exhibits a transchromatic phenomenon: the slice spectral sequence of a higher height theory is stratified into distinct regions, each isomorphic to the slice spectral sequences of the lower height theories. This provides an inductive approach and various structural insights when computing the fixed points of Lubin—Tate theories.   This is joint work with Lennart Meier and Mingcong Zeng.

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

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