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

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.