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Tate blueshift for real oriented cohomology

Banff International Research Station for Mathematical Innovation and Discovery

This is joint work with Guchuan Li and Vitaly Lorman. The Johnson--Wilson spectra $E(n)$ play a fundamental role in chromatic homotopy theory. In the late 90's, Ando--Morava--Sadofsky showed that the Tate construction with respect to a trivial $\mathbb{Z}/p$-action on $E(n)$ splits into a wedge of $E(n-1)$'s. I will describe a $C_2$-equivariant lift of this result involving the Real Johnson--Wilson theories $E\mathbb{R}(n)$ studied by Hu--Kriz and Kitchloo--Lorman--Wilson. Our result simultaneously generalizes the work of Ando--Morava--Sadofsky (by taking underlying spectra) and a classical Tate splitting for real topological K-theory proven by Greenlees--May (by taking $C_2$-fixed points). I will outline the proof and highlight an essential tool, the parametrized Tate construction (developed in joint work with Jay Shah), which has other applications relevant to the workshop.

Mathematics; Category theory; homological algebra; K-theory; Algebraic topology

video/mp4

Author affiliation: Cornell University

2020-09-22

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/76121

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/