Big Cohen-Macaulay Test Ideals on Mixed Characteristic Toric Schemes

Abstract

We provide a formula to compute the big Cohen-Macaulay test ideal for triples $((R,\Delta ),{\mathfrak{a}}^t)$ where $R$ is a mixed characteristic toric ring and $\mathfrak{a}$ is a monomial ideal. Of particular interest is that this result is consistent with the formulas for test ideals in positive characteristic and multiplier ideals in characteristic zero.

13 pages, 1 figure