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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.19704 |
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| _version_ | 1866915537205854208 |
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| author | Lampert, Amichai |
| author_facet | Lampert, Amichai |
| contents | In this note, we present an elementary proof of the fact that the slice rank of a trilinear form over a finite field is bounded above by a linear expression in the analytic rank. The existing proofs by Adiprasito-Kazhdan-Ziegler and Cohen-Moshkovitz both rely on results of Derksen via geometric invariant theory. A novel feature of our proof is that the linear forms appearing in the slice rank decomposition are obtained from the trilinear form by fixing coordinates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19704 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Slice rank and analytic rank for trilinear forms Lampert, Amichai Combinatorics Algebraic Geometry In this note, we present an elementary proof of the fact that the slice rank of a trilinear form over a finite field is bounded above by a linear expression in the analytic rank. The existing proofs by Adiprasito-Kazhdan-Ziegler and Cohen-Moshkovitz both rely on results of Derksen via geometric invariant theory. A novel feature of our proof is that the linear forms appearing in the slice rank decomposition are obtained from the trilinear form by fixing coordinates. |
| title | Slice rank and analytic rank for trilinear forms |
| topic | Combinatorics Algebraic Geometry |
| url | https://arxiv.org/abs/2404.19704 |