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 $((R,\mathrm{\Delta }),{\mathfrak{𝔞}}^t)$ 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.