Homotopy invariance of nonstable K_1functors
Abstract
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 nonstable K_1functor 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^1homotopy invariant on the category of regular kalgebras, 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 kalgebra R with the fraction field K.
 Publication:

arXiv eprints
 Pub Date:
 November 2011
 arXiv:
 arXiv:1111.4664
 Bibcode:
 2011arXiv1111.4664S
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Group Theory;
 Mathematics  KTheory and Homology;
 19B99;
 20G07;
 20G15;
 20G35
 EPrint:
 40 pages (font size enlarged)