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,Δ),𝔞t) where R is a mixed characteristic toric ring and 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.