{"paper":{"title":"Transfers for non-stable K_1-functors of classical type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Anastasia Stavrova","submitted_at":"2014-08-22T19:43:37Z","abstract_excerpt":"Let k be a field. Let G be an absolutely almost simple simply connected k-group of type A_l, l>=2, or D_l, l>=4, containing a 2-dimensional split torus. If G is of type D_l, assume moreover that char k is different from 2. We show that the Nisnevich sheafification of the non-stable K_1-functor K_1^G, also called the Whitehead group of G, on the category of smooth k-schemes is A^1-invariant, and has oriented weak transfers for affine varieties in the sense of Panin-Yagunov-Ross. If k has characteristic 0, this implies that the Nisnevich sheafification of K_1^G is birationally invariant.\n  We al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5398","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"}