Homotopy invariance of non-stable K_1-functors

By A. Stavrova. 2011

57 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3976c2899f7d6ddcc38ada4c9c26dc7c07bb5951

Citations in the corpus

• Affine representability results in 1–homotopy theory, II : Principal bundles and homogeneous spaces (2015, unknown): “Under the additional hypotheses in (ii), it follows immediately from a result of Stavrova [59, Theorem 1.3] that this surjection is an isomorphism and (ii) follows from (i).”