Article contents
On
$K(1)$-local
$\mathrm {TR}$
Published online by Cambridge University Press: 04 May 2021
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
$\mathrm {TR}$.
MSC classification
- Type
- Research Article
- Information
- Copyright
- © The Author(s) 2021
Footnotes
This work was done while the author was a Clay Research Fellow.
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