2021/02/16 by Jonas McCandless, McCandless, Jonas · 2 citations
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AT #math.KT
paper · pdf · doi:10.48550/arxiv.2102.08281
51 pages, some updates
arxiv created 2022/02/28 · arxiv updated 2022/03/01
We prove that TR is corepresentable by the reduced topological Hochschild homology of the flat affine line S[t] 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 p-typical setting. As an application, we show that TR evaluated on a connective E1-ring admits a description in terms of the spectrum of curves on algebraic K-theory generalizing the work of Hesselholt and Betley-Schlichtkrull.