{"paper":{"title":"Homotopy invariance of non-stable K_1-functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.KT"],"primary_cat":"math.AG","authors_text":"Anastasia Stavrova","submitted_at":"2011-11-20T19:01:25Z","abstract_excerpt":"Let G be reductive algebraic group over a field k, such that every semisimple normal subgroup of G has isotropic rank >=2. Let K_1^G be the non-stable K_1-functor associated to G (also called the Whitehead group of G in the field case). We show that K_1^G(k)=K_1^G(k[X_1,...,X_n]) for any n>= 1. This implies that K_1^G is A^1-homotopy invariant on the category of regular k-algebras, if k is perfect. If k is infinite perfect, one also deduces that K_1^G(R)-> K_1^G(K) is injective for any regular local k-algebra R with the fraction field K."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4664","kind":"arxiv","version":5},"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"}