Absence of torsion in orbit space

Sampat Sharma

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arXiv · 2007.07545

Absence of torsion in orbit space

Sampat Sharma

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Abstract

In this paper, we prove that if $R$ is a local ring of dimension $d,$ $d\geq 2$ and $\frac{1}{d!}\in R$ then the group $\frac{Um_{d+1}(R[X])}{E_{d+1}(R[X])}$ has no $k$-torsion, provided $k\in GL_{1}(R).$ We also prove that if $R$ is a regular ring of dimension $d,$ $d\geq 2$ and $\frac{1}{d!}\in R$ such that $E_{d+1}(R)$ acts transitively on $Um_{d+1}(R)$ then $E_{d+1}(R[X])$ acts transitively on $Um_{d+1}(R[X]).$

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Sampat Sharma. 2020-07-15. Absence of torsion in orbit space. https://arxiv.org/abs/2007.07545

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