On the hit problem for the polynomial algebra and the algebraic transfer

Dang Vo Phuc

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arXiv · 2412.02494

On the hit problem for the polynomial algebra and the algebraic transfer

Dang Vo Phuc

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Abstract

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.

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Dang Vo Phuc. 2024-12-03. On the hit problem for the polynomial algebra and the algebraic transfer. https://arxiv.org/abs/2412.02494

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