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arXiv · 2609.10180

Keller maps and holonomic $D$-modules

Wenliang Zhang
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Abstract

Let $\kk$ be a field of characteristic $p$ and $R=\kk[x_1,\dots,x_n]$. Let $D$ denote the ring of $\kk$-linear differential operators on $R$. Let $\varphi:R\to R$ be a $\kk$-algebra endomorphism whose Jacobian is a unit in $R$. We show that there is a unique $\kk$-algebra endomorphism $\Phi:D\to D$ such that $\Phi|_R=\varphi$ and that the restriction of scalar via $\Phi$ preserves holonomicity. We also construct an example of a $\kk$-algebra endomorphism of $D$ that does not preserve holonomicity.

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Wenliang Zhang. 2026-09-09. Keller maps and holonomic $D$-modules. https://arxiv.org/abs/2609.10180

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