Some arithmetic aspects of polynomial maps
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2018
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| Acceso en línea: | |
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| _version_ | 1866910629115199488 |
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| author | Mendson, Wodson |
| author_facet | Mendson, Wodson |
| contents | The Jacobian conjecture is a well-known open problem in affine algebraic geometry that asks if any polynomial endomorphism of the affine space $\mathbb{A}_{\mathbb{C}}^{n}$ ($n\geq2$) with jacobian $1$ is an automorphism. We present a survey about some results around this conjecture and we discuss an arithmetic aspect of this conjecture due to Essen-Lipton. We investigate some cases of this arithmetic approach showing the close relationship between the Jacobian Conjecture and the problem of counting $\mathbb{F}_p$-points of an affine scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1802_04247 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Some arithmetic aspects of polynomial maps Mendson, Wodson Algebraic Geometry The Jacobian conjecture is a well-known open problem in affine algebraic geometry that asks if any polynomial endomorphism of the affine space $\mathbb{A}_{\mathbb{C}}^{n}$ ($n\geq2$) with jacobian $1$ is an automorphism. We present a survey about some results around this conjecture and we discuss an arithmetic aspect of this conjecture due to Essen-Lipton. We investigate some cases of this arithmetic approach showing the close relationship between the Jacobian Conjecture and the problem of counting $\mathbb{F}_p$-points of an affine scheme. |
| title | Some arithmetic aspects of polynomial maps |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1802.04247 |