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

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arxiv 2209.05314 v1 pith:C6IULGJS submitted 2022-09-12 math.AT math.KT

Ishan Levy This is my paper · ORCID
classification math.ATmath.KT
keywords k-theoryalgebraicclasseslocalspectraspheretypecategory
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abstract

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.

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  1. On higher real $K$-theories and finite spectra

    math.KT 2025-07 conditional novelty 8.0 of 10

    At the prime 2, the connective higher real K-theories eo_h are shown to be fp spectra of type h, which implies a divisibility constraint on Euler characteristics and a new obstruction to generalized Moore spectra.

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