Maximally differential ideals of finite projective dimension

Author(s)

Miranda-Neto, Cleto B. ^[1]

Affiliation

^[1] Univ Fed Paraiba, BR-58051900 Joao Pessoa, Paraiba - Brazil

• Document type: Journal article
• Source: BULLETIN DES SCIENCES MATHEMATIQUES; v. 166, FEB 2021.
• Web of Science Citations: 0

Abstract

For decades, differential ideals have played an important role in algebra. In this paper, if A is a Noetherian local ring with positive residual characteristic, we characterize when a maximally differential ideal B subset of A is an integrally closed ideal of finite projective dimension. Our main argument yields, in a characteristic-free setting, that if B has finite projective dimension then B must be a complete intersection. This generalizes a well-known result which assumes A to be regular. We derive further homological criteria and, along the way, we conjecture (in positive residual characteristic) that if B is maximally differential with respect to the entire derivation module, then A must be a complete intersection ring if B is integrally closed and has finite complete intersection dimension. (C) 2020 Elsevier Masson SAS. All rights reserved. (AU)

• FAPESP's process: 19/21843-2 - Local cohomology, homological problems and blowup algebras
• Grantee: Victor Hugo Jorge Pérez
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil