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arXiv · 2401.11072

Inverse limits of automorphisms of truncated polynomials and applications related to Jacobian conjecture

Hao Chang·Bin Shu·Yu-Feng Yao
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Abstract

In this note, we investigate Jacobian conjecture through investigation of automorphisms of polynomial rings in characteristic $p$. Making use of the technique of inverse limits, we show that under Jacobian condition for a given homomorphism $\varphi$ of the polynomial ring $\mathbf{k}[x_1,\ldots,x_n]$, if $\varphi$ preserves the maximal ideals, then $\varphi$ is an automorphism.

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Hao Chang, Bin Shu, Yu-Feng Yao. 2024-01-20. Inverse limits of automorphisms of truncated polynomials and applications related to Jacobian conjecture. https://arxiv.org/abs/2401.11072

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