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

2024/12/03 by Đặng Võ Phúc, Phuc, Dang Vo · 1 citation
Mathematics · #55R12 #55S05 #55S10 #55T15 #Advanced Differential Equations and Dynamical Systems #Algebraic Topology (math.AT) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2412.02494

openalex publication_date 2024/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates Singer's conjecture by examining the cohit module \mathbb F₂⊗_{\mathcal A}P^{⊗ 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≥ 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.

Cited by

• The affirmative answer to Singer's conjecture on the algebraic transfer of rank four

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