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On the equality of test ideals

https://doi.org/10.1016/j.aim.2024.109559

Aberbach, Ian ; Huneke, Craig ; Polstra, Thomas ( April 2024 , Advances in Mathematics)

Free, publicly-accessible full text available April 1, 2025
Compatible ideals in ℚ-Gorenstein rings

https://doi.org/10.1090/proc/16331

Polstra, Thomas ; Schwede, Karl ( October 2023 , Proceedings of the American Mathematical Society)

Suppose $R$ is a $F$ -finite and $F$ -pure $\mathbb {Q}$ -Gorenstein local ring of prime characteristic $p>0$ . We show that an ideal $I\subseteq R$ is uniformly compatible ideal (with all $p^{-e}$ -linear maps) if and only if exists a module finite ring map $R\to S$ such that the ideal $I$ is the sum of images of all $R$ -linear maps $S\to R$ . In other words, the set of uniformly compatible ideals is exactly the set of trace ideals of finite ring maps.

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Free, publicly-accessible full text available October 1, 2024
Global F-splitting ratio of modules

De Stefani, Alessandro Yao ( July 2022 , Journal of algebra)

Full Text Available
Local Cohomology Bounds and the Weak Implies Strong Conjecture in Dimension 4

Aberbach, Ian Polstra ( June 2022 , Journal of algebra)

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