Affiliation:
1. Institut für Mathematik, Universität Osnabrück, Albrechtstraße 28a, 49076 Osnabrück, Germany
Abstract
Abstract
For every prime $p$, Mohan Kumar constructed examples of stably free modules of rank $p$ on suitable $p+1$-dimensional smooth affine varieties. This note discusses how to detect the corresponding unimodular rows by an explicit motivic cohomology group. Using the recent developments in the $\mathbb{A}^1$-obstruction classification of vector bundles, this provides an alternative proof of non-triviality of Mohan Kumar’s stably free modules. The reinterpretation of Mohan Kumar’s examples also allows to produce interesting examples of stably trivial torsors for other algebraic groups.
Publisher
Oxford University Press (OUP)