Paper
Non-Stable K1-Functors Of Discrete Valuation Rings Containing A Field
Authors
Philippe Gille, Anastasia Stavrova
Abstract
Let k be a field, and let G be a simply connected semisimple k-group which is isotropic and contains a strictly proper parabolic k-subgroup P . Let D be a discrete valuation ring which is a local ring of a smooth algebraic curve over k. Let K be the fraction field of D. We show that the corresponding non-stable K 1 -functor (for G and P,, also called the Whitehead group of G) coincide over D and K.. As a consequence, K\_G^P 1 (D) coincides with the (generalized) Manin's R-equivalence class group of G(D).