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.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | International Mathematics Research Notices |
| Vol/bind | 2024 |
| Udgave nummer | 14 |
| Sider (fra-til) | 10918-10924 |
| Antal sider | 7 |
| ISSN | 1073-7928 |
| DOI | |
| Status | Udgivet - 2024 |
Bibliografisk note
Funding Information:The second author is partially supported by the Danish National Research Foundation through the Copenhagen Centre for Geometry and Topology (DNRF151). The third author was supported by ISF1588/18, BSF 2018389 and the ERC under the European Union\u2019s Horizon 2020 research and innovation program (grant agreement no. 101125896). The fourth author was supported by ISF1848/23. Acknowledgments
Publisher Copyright:
© The Author(s) 2024. Published by Oxford University Press.