On the Equality of Test Ideals
Ian Aberbach, Craig Huneke, Thomas Polstra

TL;DR
This paper establishes a criterion ensuring the equality of finitistic and test ideals in local rings of prime characteristic, particularly for weakly F-regular rings with Noetherian anti-canonical algebras.
Contribution
It introduces a natural criterion for the equality of test ideals and demonstrates its applicability to a broad class of weakly F-regular rings.
Findings
Criterion implies equality of test ideals in certain local rings
All local weakly F-regular rings with Noetherian anti-canonical algebra meet the criterion
Enhances understanding of test ideal behavior in prime characteristic rings
Abstract
We provide a natural criterion which implies equality of the finitistic test ideal and test ideal in local rings of prime characteristic. Most notably, we show that the criterion is met by every local weakly -regular ring whose anti-canonical algebra is Noetherian on the punctured spectrum.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · Advanced Topics in Algebra
