Reducedness of formally unramified algebras over fields

We prove that under suitable graded and local hypothesis, a formally unramified algebra over a field must be reduced. We detail examples, including one due to Gabber, to show that it is not possible to generalize these results further.

Saved in:
Bibliographic Details
Published in:Journal of algebra 2021-07, Vol.577, p.61-73
Main Authors: Mukhopadhyay, Alapan, Smith, Karen E.
Format: Article
Language:English
Subjects:
Graded rings
Kahler differentials
Noetherian unramified algebras
Nonreduced unramified algebras
Universal derivation
Unramified algebras
Unramified algebras are reduced
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove that under suitable graded and local hypothesis, a formally unramified algebra over a field must be reduced. We detail examples, including one due to Gabber, to show that it is not possible to generalize these results further.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2021.03.002