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arXiv · 2111.10837

Examples of chromatic redshift in algebraic $K$-theory

Allen Yuan
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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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Allen Yuan. 2021-11-21. Examples of chromatic redshift in algebraic $K$-theory. https://arxiv.org/abs/2111.10837

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