arXiv:2209.05314 Abstract | arXiv Analytics

arXiv:2209.05314 [math.AT]Abstract References Reviews Resources

The algebraic K-theory of the K(1)-local sphere via TC

Published 2022-09-12Version 1

We describe the algebraic K-theory of the $K(1)$-local sphere and the category of type 2 finite spectra in terms of K-theory of discrete rings and topological cyclic homology. We find an infinite family of 2-torsion classes in the $K_0$ of type 2 spectra at the prime 2, and explain how to construct representatives of these $K_0$ classes.

Comments: 30 pages, comments welcome!

Categories: math.AT, math.KT

Keywords: algebraic k-theory, construct representatives, local sphere, finite spectra, topological cyclic homology

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