The perfection can be a non-coherent GCD domain
Commutative Algebra
2024-01-02 v1
Abstract
We show that there exists a complete local Noetherian normal domain of prime characteristic whose perfection is a non-coherent GCD domain, answering a question of Patankar in the negative concerning characterizations of -coherent rings. This recovers and extends a result of Glaz using tight closure methods.
Cite
@article{arxiv.2401.00803,
title = {The perfection can be a non-coherent GCD domain},
author = {Austyn Simpson},
journal= {arXiv preprint arXiv:2401.00803},
year = {2024}
}
Comments
6 pages, comments welcome. To appear in J. Commut. Algebra