{"paper":{"title":"Framed correspondences and the Milnor-Witt K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexander Neshitov","submitted_at":"2014-10-27T20:18:25Z","abstract_excerpt":"The article is to construct a graded ring isomorphism between $H_0(ZF(\\Delta^{\\bullet}_k,\\mathbb{G}_m^{\\wedge *}))$ and the Milnor-Witt K-theory ring $K^{MW}_{*\\geqslant 0}(k)$, where $k$ is a field of characteristic zero and $ZF_*(k)$ is the category of linear framed correspondences of algebraic k-varieties, introduced by Garkusha and Panin. As it was shown by Garkusha and Panin, this partially recovers the computation of the motivic cohomotopy groups ${\\pi}^{n,n}(\\Sigma^{\\infty}_{S^1}\\Sigma^{\\infty}_{\\mathbb{G}_m}S^0)(k)$, which is originally due to Morel."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7417","kind":"arxiv","version":3},"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"}