Test Ideals in Mixed Characteristic via the p-adic Riemann-Hilbert Correspondence

Linquan Ma

Multiplier ideals in characteristic zero and test ideals in positive characteristic are fundamental objects in the study of commutative algebra and birational geometry in equal characteristic.  We introduced a mixed characteristic version of the multiplier / test ideal using the p-adic Riemann-Hilbert correspondence of Bhatt-Lurie.  Under mild finiteness assumptions, we show that this version of test ideal commutes with localization and can be computed by a single alteration up to small perturbation.   This is based on joint work in progress with Bhargav Bhatt, Zsolt Patakfalvi, Karl Schwede, Kevin Tucker, Joe Waldron, and Jakub Witaszek.

https://www.ias.edu/video/test-ideals-mixed-characteristic-p-adic-riemann-hilbert-correspondence