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Examples of chromatic redshift in algebraic $K$-theory

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arxiv 2111.10837 v1 pith:5P27WCX7 submitted 2021-11-21 math.KT math.AT

Allen Yuan This is my paper · ORCID
classification math.KTmath.AT
keywords theoryalgebraicchromaticgivelocalizationnontrivialredshiftapplications
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abstract

We give a simple argument to detect chromatic redshift in the algebraic $K$-theory of $\mathbb{E}_{\infty}$-ring spectra and give two applications: we show for $n\geq 1$ that $K(E_n)$, 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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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Chromatic Purity in Hermitian K-Theory at $p=2$

    math.KT 2025-01 reject novelty 6.0 of 10

    At p=2, L-theory of rings with anti-involution is claimed to have no chromatic redshift and to satisfy a chromatic purity theorem.

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