{"paper":{"title":"Chromatic Purity in Hermitian K-Theory at $p=2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.KT","authors_text":"Jordan Levin","submitted_at":"2025-01-16T16:21:01Z","abstract_excerpt":"In this article we investigate the question of chromatic purity of L-theory. To do so, we utilize the theory of additive GW and L-theory in the language of Poincar\\'e categories as laid out in the series of papers by Calm\\`es et al. We apply this theory to chromatically localised L-theory at the prime $p=2$ and recover the L-theoretic analogues of chromatic purity for $E_1$-rings with involution. From this, we deduce that L-theory does not exhibit chromatic redshift. We deduce the higher chromatic vanishing of quadratic L-theory of arbitrary idempotent complete categories, thereby allowing the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.09633","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/2501.09633/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"}