PreprintCC BY 4.0arXiv
Descent along flat composed with radicalization
Abstract
We study the following general situation. Let R→ S be a finite flat morphism of regular rings of zero (resp. prime) characteristic. For P∈ Spec R, put A=R/P, C=S/PS, and B=S/√(PS)=Cred. 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→ C, whereas the passage C→ Cred may destroy nilpotent information.
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BibTeX
@misc{asgharzadeh2026descent,
title = {{Descent along flat composed with radicalization}},
author = {Mohsen Asgharzadeh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24577},
eprint = {2609.24577},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24577},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Descent along flat composed with radicalization
AU - Mohsen Asgharzadeh
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.24577
UR - https://arxiv.org/abs/2609.24577
AB - We study the following general situation. Let R→ S be a finite flat morphism of regular rings of zero (resp. prime) characteristic. For P∈ Spec R, put A=R/P, C=S/PS, and B=S/√(PS)=C_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→ C, whereas the passage C→ C_red may destroy nilpotent information.
ER -