{"paper":{"title":"Motivic spheres and the image of the Suslin--Hurewicz map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT","math.GR"],"primary_cat":"math.KT","authors_text":"Aravind Asok, Ben Williams, Jean Fasel","submitted_at":"2018-04-13T17:00:32Z","abstract_excerpt":"We show that an old conjecture of A.A. Suslin characterizing the image of a Hurewicz map from Quillen K-theory in degree $n$ to Milnor K-theory in degree $n$ admits an interpretation in terms of unstable ${\\mathbb A}^1$-homotopy sheaves of the general linear group. Using this identification, we establish Suslin's conjecture in degree $5$ for infinite fields having characteristic unequal to $2$ or $3$. We do this by linking the relevant unstable ${\\mathbb A}^1$-homotopy sheaf of the general linear group to the stable ${\\mathbb A}^1$-homotopy of motivic spheres."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05030","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":""},"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"}