Let $ X $ be an integral scheme of finite type over a complete DVR of mixed characteristic.
We provide a definition of a test ideal which agrees with the multiplier ideal after inverting …

We prove a uniform bound on the growth of symbolic powers of arbitrary (not necessarily
radical) ideals in arbitrary (not necessarily excellent) regular rings of all characteristics. This …

We develop a duality for operations on nested pairs of modules that generalizes the duality
between absolute interior operations and residual closure operations from [5], extending our …

Exploiting the interior-closure duality developed by Epstein and RG [10], we show that for
the class of Matlis dualizable modules M over a Noetherian local ring, when cl is a …

A splinter is a notion of singularity that has seen numerous recent applications, especially in
connection with the direct summand theorem, the mixed characteristic minimal model …

A local Cohen--Macaulay ring is called Ulrich-split if any short exact sequence of Ulrich
modules split. In this paper we initiate the study of Ulrich split rings. We prove several …

We define a duality operation connecting closure operations, interior operations, and test
ideals, and describe how the duality acts on common constructions such as trace, torsion …

BIG COHEN–MACAULAY TEST IDEALS IN EQUAL CHARACTERISTIC ZERO VIA
ULTRAPRODUCTS Page 1 Nagoya Math. J., 251 (2023), 549–575 DOI 10.1017/nmj.2022.41 …

We develop the theory of trace modules up to isomorphism and explore the relationship
between preenveloping classes of modules and the property of being a trace module …

We characterize adjoint ideal sheaves via ultraproducts and, utilizing this characterization,
study their behavior under pure morphisms. In particular, given a pure morphism $ f: Y\to X …