@article{SMOLKIN20201132,
title = {A new subadditivity formula for test ideals},
journal = {Journal of Pure and Applied Algebra},
volume = {224},
number = {3},
pages = {1132-1172},
year = {2020},
issn = {0022-4049},
doi = {https://doi.org/10.1016/j.jpaa.2019.07.010},
url = {https://www.sciencedirect.com/science/article/pii/S0022404919301811},
author = {Daniel Smolkin},
keywords = {-singularities, Test ideals, Multiplier ideals, Cartier algebras, Toric varieties},
abstract = {We exhibit a new subadditivity formula for test ideals on singular varieties using an argument similar to [9] and [16]. Any subadditivity formula for singular varieties must have a correction term that measures the singularities of that variety. Whereas earlier subadditivity formulas accomplished this by multiplying by the Jacobian ideal, our approach is to use the formalism of Cartier algebras [1]. We also show that our subadditivity containment is sharper than ones shown previously in [32] and [11]. The first of these results follows from a Noether normalization technique due to Hochster and Huneke. The second of these results is obtained using ideas from [33] and [11] to show that the adjoint ideal JX(A,Z) reduces mod p to Takagi's adjoint test ideal, even when the ambient space is singular, provided that A is regular at the generic point of X. One difficulty of using this new subadditivity formula in practice is the computational complexity of computing its correction term. Thus, we discuss a combinatorial construction of the relevant Cartier algebra in the toric setting.}
}