Correspondences and stable homotopy theory

A general method of producing correspondences and spectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra SH$SH$ is recovered from modules over a commutative symmetric ring spectrum defined in terms of framed corresponden...

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Bibliographic Details
Published in:Transactions of the London Mathematical Society 2023-12, Vol.10 (1), p.124-155
Main Author: Garkusha, Grigory
Format: Article
Language:English
Subjects:
Algebra
Categories
Homotopy theory
Modules
Production methods
Rings (mathematics)
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Summary:A general method of producing correspondences and spectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra SH$SH$ is recovered from modules over a commutative symmetric ring spectrum defined in terms of framed correspondences over an algebraically closed field. Another application recovers stable motivic homotopy theory SH(k)$SH(k)$ from spectral modules over associated spectral categories.
ISSN:2052-4986
2052-4986
DOI:10.1112/tlm3.12056