The Segal conjecture for topological Hochschild homology of Ravenel spectra

Angelini-Knoll, Gabriel; Quigley, J.D.

doi:10.1007/s40062-021-00275-7

Cited by 5 publications

(2 citation statements)

References 30 publications

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“…Chromatic redshift has since been studied extensively: in height 1 examples such as ku ∧ p , KU ∧ p and ku/p by [BM08, Aus10, AR02, AR12]; computationally in [AK17, AKQ21,Vee18] and via theoretical considerations [Wes17,CSY21]; additionally, questions of descent were addressed in the foundational papers [CMNN20a,CM19]. This work builds upon recent progress by Land-Mathew-Meier-Tamme [LMMT20] and Clausen-Mathew-Naumann-Noel [CMNN20b]: to motivate it, we sample a result of [CMNN20b] which generalizes a theorem of Mitchell [Mit90] in the case n = 1:…”

Section: Introductionmentioning

confidence: 99%

Examples of chromatic redshift in algebraic $K$-theory

Yuan¹

2021

Preprint

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We give a simple argument to detect chromatic redshift in the algebraic K-theory of E∞-ring spectra and give two applications: we show for n ≥ 1 that K(En), the algebraic K-theory of any height n Lubin-Tate theory, has nontrivial T (n + 1)-localization, and that K (n) (k), the n-fold iterated algebraic K-theory of a field k of characteristic different from p, has nontrivial T (n)-localization.

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Section: Introductionmentioning

confidence: 99%

Examples of chromatic redshift in algebraic $K$-theory

Yuan¹

2021

Preprint

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“…However, all previous work on Quillen-Lichtenbaum conjectures for ring spectra have been based on periodic homotopy groups and the finite telescopic localization functors L f n (see, for example, [25] for a definition). In particular, Rognes' redshift conjectures [30, p. 8], [32, 4.1(a)], [20, 6.0.5] and results in this direction by Angelini-Knoll [3], Angelini-Knoll-Quigley [2], Ausoni-Rognes [4], Carmeli-Schlank-Yanovski [12], Clausen-Mathew-Naumann-Noel [13], Hahn-Wilson [20], Land-Mathew-Meier-Tamme [23], and Veen [36] ask or answer the following question about particular ring spectra R:…”

Section: Introductionmentioning

confidence: 99%

Chromatic convergence for the algebraic K-theory of the sphere spectrum

Blumberg¹,

Mandell²,

Yuan³

2021

Preprint

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On -local

Mathew¹

2021

Compositio Math.

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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 $\mathrm {TR}$ .

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The Segal conjecture for topological Hochschild homology of Ravenel spectra

Cited by 5 publications

References 30 publications

Examples of chromatic redshift in algebraic $K$-theory

Examples of chromatic redshift in algebraic $K$-theory

Chromatic convergence for the algebraic K-theory of the sphere spectrum

On -local

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