On the hit problem for the polynomial algebra and the algebraic transfer
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916955846344704 |
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| author | Phuc, Dang Vo |
| author_facet | Phuc, Dang Vo |
| contents | This paper investigates Singer's conjecture by examining the cohit module $\mathbb F_2\otimes_{\mathcal A}P^{\otimes h}$ for specific degrees and values of $h$. Utilizing hit problem techniques, we extend previous work by Mothebe et al. and establish key dimensional results. Notably, for $h\geq 6$, we prove that the cohit module's dimension in certain degrees matches the order of a specific factor group. Our contributions include demonstrating that certain non-zero elements do not belong to the image of the Singer algebraic transfer. All results were verified using the OSCAR computer algebra system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02494 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the hit problem for the polynomial algebra and the algebraic transfer Phuc, Dang Vo Algebraic Topology 55S05, 55S10, 55R12, 55T15 This paper investigates Singer's conjecture by examining the cohit module $\mathbb F_2\otimes_{\mathcal A}P^{\otimes h}$ for specific degrees and values of $h$. Utilizing hit problem techniques, we extend previous work by Mothebe et al. and establish key dimensional results. Notably, for $h\geq 6$, we prove that the cohit module's dimension in certain degrees matches the order of a specific factor group. Our contributions include demonstrating that certain non-zero elements do not belong to the image of the Singer algebraic transfer. All results were verified using the OSCAR computer algebra system. |
| title | On the hit problem for the polynomial algebra and the algebraic transfer |
| topic | Algebraic Topology 55S05, 55S10, 55R12, 55T15 |
| url | https://arxiv.org/abs/2412.02494 |