Year: 2026
Type: preprint
Abstract: We study the following general situation. Let $R\to S$ be a finite flat morphism of regular rings of zero (resp. prime) mixed or (equi)-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 (not) destroy nilpotent information.
Source: arXiv (Cornell University)
Author: Asgharzadeh, Mohsen
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214047924