Test ideals were first introduced by Mel Hochster and Craig Huneke in their celebrated
theory of tight closure, and since their invention have been closely tied to the theory of …

We give characterizations of test ideals and $ F $-rational singularities via (regular)
alterations. Formally, the descriptions are analogous to standard characterizations of …

In recent years, multiplier ideals have played an increasingly important role in higher-
dimensional birational geometry. For a given ideal a on a smooth variety X and a real …

The local theory of prime characteristic singularities is a beautiful and historied subject.
Singularities which are defined in terms of the behavior of the Frobenius endomorphism …

We study the behavior of test ideals and F-singularities in families. In particular, we obtain
generic (and non-generic) restriction theorems for test ideals and non-F-pure ideals which …

For a normal F-finite variety $ X $ and a boundary divisor $\Delta $ we give a uniform
description of an ideal which in characteristic zero yields the multiplier ideal, and in positive …

This paper presents three results on F-singularities. First, we give a new proof of Eisenstein's
restriction theorem for adjoint ideal sheaves using the theory of F-singularities. Second, we …

We study the behavior of test ideals and F-singularities in families. In particular, we obtain
generic (and non-generic) restriction theorems for test ideals and non-F-pure ideals …

Two different ideals have been defined during the last decade, each of which has played an
important role in its respective area. In commutative algebra, the test ideal defined by …

The multiplicity is an important first step in measuring singularities, but it is too crude to give
a good measurement. This paper describes the first steps toward understanding a much …