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K -theoretic counterexamples to R avenel's telescope conjecture

Robert Burklund, Jeremy Hahn, Ishan Levy, Tomer M · 2023 · math.AT · arXiv 2310.17459

6 Pith papers cite this work. Polarity classification is still indexing.

6 Pith papers citing it
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abstract

At each prime $p$ and height $n+1 \ge 2$, we prove that the telescopic and chromatic localizations of spectra differ. Specifically, for $\mathbb{Z}$ acting by Adams operations on $\mathrm{BP}\langle n \rangle$, we prove that the $T(n+1)$-localized algebraic $K$-theory of $\mathrm{BP}\langle n \rangle^{h\mathbb{Z}}$ is not $K(n+1)$-local. We also show that Galois hyperdescent, $\mathbb{A}^1$-invariance, and nil-invariance fail for the $K(n+1)$-localized algebraic $K$-theory of $K(n)$-local $\mathbb{E}_{\infty}$-rings. In the case $n=1$ and $p \ge 7$ we make complete computations of $T(2)_*\mathrm{K}(R)$, for $R$ certain finite Galois extensions of the $K(1)$-local sphere. We show for $p\geq 5$ that the algebraic $K$-theory of the $K(1)$-local sphere is asymptotically $L_2^{f}$-local.

fields

math.AT 5 math.KT 1

years

2026 4 2025 1 2024 1

verdicts

UNVERDICTED 4 ACCEPT 1 unreviewed 1

representative citing papers

Structured Real Snaith Equivalences

math.AT · 2026-06-22 · accept · novelty 7.0

Structured Real Snaith equivalences hold as EC2∞- and Eρ-algebra maps, enabling THR computations for KUR and MUPR via a norm-inverted variant.

On periodic homotopy and homology equivalences of spaces

math.AT · 2026-04-13 · unverdicted · novelty 7.0

Precise comparisons are established between T(n)-homology and v_n-periodic homotopy equivalences, including a T(n)-local version of Kuhn's result and a formula for L_n^f-localization of infinite loop spaces from spectra with L_{n-1}^f vanishing.

Structured Quotients in Real Homotopy Theory

math.AT · 2026-06-24 · unverdicted · novelty 6.0

Authors construct ring involution structures on quotients of Real bordism, orient Lubin-Tate theory via truncated Brown-Peterson spectra, and characterize equivalences after chromatic localization.

citing papers explorer

Showing 6 of 6 citing papers.

  • Structured Real Snaith Equivalences math.AT · 2026-06-22 · accept · none · ref 29

    Structured Real Snaith equivalences hold as EC2∞- and Eρ-algebra maps, enabling THR computations for KUR and MUPR via a norm-inverted variant.

  • On periodic homotopy and homology equivalences of spaces math.AT · 2026-04-13 · unverdicted · none · ref 2

    Precise comparisons are established between T(n)-homology and v_n-periodic homotopy equivalences, including a T(n)-local version of Kuhn's result and a formula for L_n^f-localization of infinite loop spaces from spectra with L_{n-1}^f vanishing.

  • Algebraic K-theory of finite algebras over higher local fields math.KT · 2025-03-26 · unverdicted · none · ref 1

    Segal conjecture fails for truncated polynomial algebras over higher chromatic local fields, causing Lichtenbaum-Quillen property to fail while weak redshift conjecture holds.

  • New simple $\eta$-torsion families of elements in the stable stems math.AT · 2024-10-28 · unverdicted · none · ref 7

    Produces five 192-periodic families of simple η-torsion elements in stable stems with trivial tmf-Hurewicz image and shows several other families are simple η-torsion.

  • Structured Quotients in Real Homotopy Theory math.AT · 2026-06-24 · unverdicted · none · ref 36

    Authors construct ring involution structures on quotients of Real bordism, orient Lubin-Tate theory via truncated Brown-Peterson spectra, and characterize equivalences after chromatic localization.

  • Higher Semiadditive Character Theory math.AT · 2026-07-08 · unreviewed · ref 44 · internal anchor