{"paper":{"title":"$K$-theoretic counterexamples to Ravenel's telescope conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Ishan Levy, Jeremy Hahn, Robert Burklund, Tomer M. Schlank","submitted_at":"2023-10-26T15:07:07Z","abstract_excerpt":"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)_*\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.17459","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.17459/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}