Absence of torsion in orbit space
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866909018251853824 |
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| author | Sharma, Sampat |
| author_facet | Sharma, Sampat |
| contents | 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 $Um_{d+1}(R[X]).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_07545 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Absence of torsion in orbit space Sharma, Sampat Commutative Algebra 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 $Um_{d+1}(R[X]).$ |
| title | Absence of torsion in orbit space |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2007.07545 |