Abstract
We discuss some general properties of $\mathrm {TR}$ and its $K(1)$-localization. We prove that after $K(1)$-localization, $\mathrm {TR}$ of $H\mathbb {Z}$-algebras is a truncating invariant in the Land–Tamme sense, and deduce $h$-descent results. We show that for regular rings in mixed characteristic, $\mathrm {TR}$ is asymptotically $K(1)$-local, extending results of Hesselholt and Madsen. As an application of these methods and recent advances in the theory of cyclotomic spectra, we construct an analog of Thomason's spectral sequence relating $K(1)$-local $K$-theory and étale cohomology for $K(1)$-local $\mathrm {TR}$.
Subject
Algebra and Number Theory
Reference76 articles.
1. Affine analog of the proper base change theorem
2. CM19 Clausen, D. and Mathew, A. , Hyperdescent and étale K-theory, Invent. Math., to appear. Preprint (2019), arXiv:1905.06611.
3. Descent in algebraic $K$-theory and a conjecture of Ausoni–Rognes
4. ČS19 Česnavičius, K. and Scholze, P. , Purity for flat cohomology, Preprint (2019), arXiv:1912.10932.
5. Filtered topological cyclic homology and relative K–theory of nilpotent ideals
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