Variations in \mathbbA¹ on a theme of Mohan Kumar

2017/04/01 by Wendt, Matthias
#14F42 (13C13 #19A13) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.00141

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 in motivic cohomology. Using the recent developments in the \mathbbA¹-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.

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