Suppose that $ X $ is an integral scheme (quasi-) projective over a complete local ring of
mixed characteristic. Using ideas of Takamatsu-Yoshikawa and Bhatt-Ma-et. al, we define a …

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 provide a natural criterion that implies equality of the test ideal and big test ideal in local
rings of prime characteristic. Most notably, we show that the criterion is met by every local …

The generalized test ideals introduced in [HY] are related to multiplier ideals via reduction to
characteristic p. In addition, they satisfy many of the subtle properties of the multiplier ideals …

Let $ S $ be an $ F $-finite regular local ring and $ I $ an ideal contained in $ S $. Let $ R=
S/I $. Fedder proved that $ R $ is $ F $-pure if and only if $(I^{[p]}: I)\nsubseteq\mathfrak …

Abstract Let (X,\varDelta)(X, Δ) be a log pair in characteristic p> 0 p> 0 and P be a (not
necessarily closed) point of X. We show that there exists a constant δ> 0 δ> 0 such that the …

Let I be a finitely supported complete m-primary ideal of a regular local ring (R, m). A
theorem of Lipman implies that I has a unique factorization as a⁎-product of special⁎-simple …

This paper gives an explicit formula for the multiplier ideals, and consequently for the log
canonical thresholds, of any GL (V)× GL (W)-invariant ideal in S= Sym (V⊗ W⁎), where V …

Given an ideal a⊆ R in a (log) Q-Gorenstein F-finite ring of characteristic p> 0, we study and
provide a new perspective on the test ideal τ (R, at) for a real number t> 0. Generalizing a …

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 …