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arXiv · 1704.00141

Variations in $\mathbb{A}^1$ on a theme of Mohan Kumar

Matthias Wendt
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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 $\mathbb{A}^1$-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.

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Matthias Wendt. 2017-04-01. Variations in $\mathbb{A}^1$ on a theme of Mohan Kumar. https://arxiv.org/abs/1704.00141

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