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

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnae109

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title = "Chromatic Cardinalities via Redshift",

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.",

author = "Shay Ben-Moshe and Shachar Carmeli and Schlank, \{Tomer M.\} and Lior Yanovski",

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doi = "10.1093/imrn/rnae109",

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AU - Ben-Moshe, Shay

AU - Carmeli, Shachar

AU - Schlank, Tomer M.

AU - Yanovski, Lior

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Y1 - 2024/7/1

N2 - 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.

AB - 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.

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DO - 10.1093/imrn/rnae109

M3 - مقالة

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SP - 10918

EP - 10924

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 14

ER -

Chromatic Cardinalities via Redshift

Abstract

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