The algebraic K-theory of the K(1)-local sphere via TC
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 K0 of type 2 spectra at the prime 2, and explain how to construct representatives of these K0 classes.
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