{"paper":{"title":"On Voevodsky's algebraic K-theory spectrum BGL","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"I. Panin, K. Pimenov, O. R\\\"ondigs","submitted_at":"2007-09-25T10:04:42Z","abstract_excerpt":"Under a certain normalization assumption we prove that the $\\Pro^1$-spectrum $\\mathrm{BGL}$ of Voevodsky which represents algebraic $K$-theory is unique over $\\Spec(\\mathbb{Z})$. Following an idea of Voevodsky, we equip the $\\Pro^1$-spectrum $\\mathrm{BGL}$ with the structure of a commutative $\\Pro^1$-ring spectrum in the motivic stable homotopy category. Furthermore, we prove that under a certain normalization assumption this ring structure is unique over $\\Spec(\\mathbb{Z})$. For an arbitrary Noetherian scheme $S$ of finite Krull dimension we pull this structure back to obtain a distinguished "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.3905","kind":"arxiv","version":2},"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/0709.3905/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"}