Chromatic Cardinalities via Redshift

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

doi:10.1093/imrn/rnae109

Chromatic Cardinalities via Redshift

Shay Ben-Moshe
, Shachar Carmeli
, Tomer M. Schlank
, Lior Yanovski^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Using higher descent for chromatically localized algebraic K-theory, we show that the higher semiadditive cardinality of a π-finite p-space A at the Lubin–Tate spectrum En is equal to the higher semiadditive cardinality of the free loop space LA at En−1. By induction, it is thus equal to the homotopy cardinality of the n-fold free loop space LⁿA. We explain how this allows one to bypass the Ravenel–Wilson computation in the proof of the ∞-semi-additivity of the T(n)-local categories.

Original language	English
Pages (from-to)	10918-10924
Number of pages	7
Journal	International Mathematics Research Notices
Volume	2024
Issue number	14
DOIs	https://doi.org/10.1093/imrn/rnae109
State	Published - 1 Jul 2024

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© The Author(s) 2024. Published by Oxford University Press.

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Chromatic Cardinalities via Redshift

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