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arXiv · 2310.04388

A chromatic vanishing result for TR

Liam Keenan·Jonas McCandless
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Abstract

In this note, we establish a vanishing result for telescopically localized $\mathrm{TR}$. More precisely, we prove that $T(k)$-local $\mathrm{TR}$ vanishes on connective $L_n^{p,f}$-acyclic $\mathbf{E}_1$-rings for every $1 \leq k \leq n$ and deduce consequences for connective Morava K-theory and the Thom spectra $y(n)$. The proof relies on the relationship between $\mathrm{TR}$ and the spectrum of curves on K-theory together with fact that algebraic K-theory preserves infinite products of additive $\infty$-categories which was recently established by C\'{o}rdova Fedeli.

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Liam Keenan, Jonas McCandless. 2023-10-06. A chromatic vanishing result for TR. https://arxiv.org/abs/2310.04388

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