An Algebraic characterization of the affine three space in arbitrary characteristic
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916235869945856 |
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| author | Krishna, P. M. S. Sai |
| author_facet | Krishna, P. M. S. Sai |
| contents | We give an algebraic characterization of the affine $3$-space over an algebraically closed field of arbitrary characteristic. We use this characterization to reformulate the following question. Let $$A=k[X, Y, Z, T]/(XY+Z^{p^e}+T+T^{sp})$$ where $p^e\nmid sp$, $sp\nmid p^e$, $e, s\geq 1$ and $k$ is an algebraically closed field of positive characteristic $p$. Is $A= k^{[3]}$? We prove some results on ML and ML$^*$ invariants and use them to prove a special case of the strong cancellation of $k^{[2]}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05424 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Algebraic characterization of the affine three space in arbitrary characteristic Krishna, P. M. S. Sai Commutative Algebra Algebraic Geometry 14R10, 13B25, 13A50, 13N15, 14R20 We give an algebraic characterization of the affine $3$-space over an algebraically closed field of arbitrary characteristic. We use this characterization to reformulate the following question. Let $$A=k[X, Y, Z, T]/(XY+Z^{p^e}+T+T^{sp})$$ where $p^e\nmid sp$, $sp\nmid p^e$, $e, s\geq 1$ and $k$ is an algebraically closed field of positive characteristic $p$. Is $A= k^{[3]}$? We prove some results on ML and ML$^*$ invariants and use them to prove a special case of the strong cancellation of $k^{[2]}$. |
| title | An Algebraic characterization of the affine three space in arbitrary characteristic |
| topic | Commutative Algebra Algebraic Geometry 14R10, 13B25, 13A50, 13N15, 14R20 |
| url | https://arxiv.org/abs/2308.05424 |