Applications of Swan's Bertini to unimodular rows
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912984426610688 |
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| author | Keshari, Manoj K. Sharma, Sampat |
| author_facet | Keshari, Manoj K. Sharma, Sampat |
| contents | Let $R$ be an affine algebra of dimension $d\geq 4$ over a perfect field $k$ of char $\neq 2$ and $I$ be an ideal of $R$. Then
- Um$_{d+1}(R,I)/{\rm E}_{d+1}(R,I)$ has nice group structure if $c.d._2(k)\leq 2$.
- Um$_d(R,I)/{\rm E}_d(R,I)$ has nice group structure if $k$ is algebraically closed of char $k\neq 2,3$ and either (i) $k = \overline{\mathbb{F}}_{p}$ or (ii) $R$ is normal.
- $MS_{d+1}(R)$ is uniquely divisible prime to characteristic of $k$ if $R$ is reduced and $k$ is infinite with $c.d.(k)\leq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_11132 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Applications of Swan's Bertini to unimodular rows Keshari, Manoj K. Sharma, Sampat K-Theory and Homology Commutative Algebra Let $R$ be an affine algebra of dimension $d\geq 4$ over a perfect field $k$ of char $\neq 2$ and $I$ be an ideal of $R$. Then - Um$_{d+1}(R,I)/{\rm E}_{d+1}(R,I)$ has nice group structure if $c.d._2(k)\leq 2$. - Um$_d(R,I)/{\rm E}_d(R,I)$ has nice group structure if $k$ is algebraically closed of char $k\neq 2,3$ and either (i) $k = \overline{\mathbb{F}}_{p}$ or (ii) $R$ is normal. - $MS_{d+1}(R)$ is uniquely divisible prime to characteristic of $k$ if $R$ is reduced and $k$ is infinite with $c.d.(k)\leq 1$. |
| title | Applications of Swan's Bertini to unimodular rows |
| topic | K-Theory and Homology Commutative Algebra |
| url | https://arxiv.org/abs/2112.11132 |