Descent along flat composed with radicalization

Mohsen Asgharzadeh

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arXiv · 2609.24577

Descent along flat composed with radicalization

Mohsen Asgharzadeh

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Abstract

We study the following general situation. Let $R\to S$ be a finite flat morphism of regular rings of zero (resp. prime) characteristic. For $P\in Spec R$, put $A=R/P, C=S/PS,$ and $B=S/\sqrt{PS}=C_{\mathrm{red}}.$ The basic question is whether a property of $B$ forces the same property of $A$. The main point is that ordinary finite-flat descent applies naturally to $A\to C$, whereas the passage $C\to C_{\mathrm{red}}$ may destroy nilpotent information.

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Mohsen Asgharzadeh. 2026-09-21. Descent along flat composed with radicalization. https://arxiv.org/abs/2609.24577

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