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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.07607 |
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| _version_ | 1866916608376569856 |
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| author | Aliyari, Saba |
| author_facet | Aliyari, Saba |
| contents | This paper creates a link between \textit{Tropical Geometry} and \textit{Difference Algebra}. The main result is a difference version of \textit{Kapranov's Theorem}. In this theorem, we extend Kapranov's Theorem to the case of a Laurent difference polynomial with coefficients from a multiplicative valued difference field, where the residue field is an algebraically closed field with a generic automorphism (ACFA). A result of this paper that plays a critical role in the proof of the Difference Kapranov Theorem is a difference version of \textit{Newton's Lemma}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Difference Kapranov Theorem Aliyari, Saba Algebraic Geometry Logic 14T10, 12H10 (Primary) 12L12, 12J10 (Secondary) This paper creates a link between \textit{Tropical Geometry} and \textit{Difference Algebra}. The main result is a difference version of \textit{Kapranov's Theorem}. In this theorem, we extend Kapranov's Theorem to the case of a Laurent difference polynomial with coefficients from a multiplicative valued difference field, where the residue field is an algebraically closed field with a generic automorphism (ACFA). A result of this paper that plays a critical role in the proof of the Difference Kapranov Theorem is a difference version of \textit{Newton's Lemma}. |
| title | The Difference Kapranov Theorem |
| topic | Algebraic Geometry Logic 14T10, 12H10 (Primary) 12L12, 12J10 (Secondary) |
| url | https://arxiv.org/abs/2502.07607 |