On curves in K-theory and TR

  • Jonas McCandless

    Max Planck Institute for Mathematics, Bonn, Germany
On curves in K-theory and TR cover
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We prove that TR is corepresentable by the reduced topological Hochschild homology of the flat affine line as a functor defined on the -category of cyclotomic spectra with values in the -category of spectra with Frobenius lifts, refining a result of Blumberg–Mandell. We define the notion of an integral topological Cartier module using Barwick’s formalism of spectral Mackey functors on orbital -categories, extending the work of Antieau–Nikolaus in the -typical setting. As an application, we show that TR evaluated on a connective -ring admits a description in terms of the spectrum of curves on algebraic K-theory, generalizing the work of Hesselholt and Betley–Schlichtkrull.

Cite this article

Jonas McCandless, On curves in K-theory and TR. J. Eur. Math. Soc. (2023), published online first

DOI 10.4171/JEMS/1347