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arXiv · 2310.00275

Chromatic Cardinalities via Redshift

Shay Ben-Moshe·Shachar Carmeli·Tomer M. Schlank·Lior Yanovski
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Abstract

Using higher descent for chromatically localized algebraic $K$-theory, we show that the higher semiadditive cardinality of a $\pi$-finite $p$-space $A$ at the Lubin-Tate spectrum $E_n$ is equal to the higher semiadditive cardinality of the free loop space $LA$ at $E_{n-1}$. By induction, it is thus equal to the homotopy cardinality of the $n$-fold free loop space $L^n A$. We explain how this allows one to bypass the Ravenel-Wilson computation in the proof of the $\infty$-semiadditivity of the $T(n)$-local categories.

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Shay Ben-Moshe, Shachar Carmeli, Tomer M. Schlank, Lior Yanovski. 2023-09-30. Chromatic Cardinalities via Redshift. https://doi.org/10.1093/imrn%2Frnae109

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