The notions of F-rational and F-regular rings are defined via tight closure, which is a closure
operation for ideals in a commutative ring of positive characteristic. The geometric …

In this paper, we investigate the relationship of F-regular (resp. F-pure) rings and log
terminal (resp. log canonical) singularities. Also, we extend the notions of F-regularity and F …

We investigate singularities which are $ F $-pure (respectively $ F $-pure type). A ring $ R $
of characteristic $ p $ is $ F $-pure if for every $ R $-module $ M, 0\to M\otimes R\to …

The notion of tight closure of an ideal introduced by Hochster and Huneke [5] enables us to
define classes of singularities corresponding to rational singularities in characteristic 0 for …

The notions of F-regularity and F-purity for rings of characteristic p> 0, which are introduced
by Hochster and Huneke [HH1] and Hochster and Roberts [HR], respectively, are now …

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

1. Introduction. Recall that if (-R, m) is a local ring which is essentially of finite type over a
field k of characteristic 0, then R is said to be of F-injective type (in the sense of Hochster …

In recent years, some very interesting theorems have been proven independently using
complex analytic techniques or, alternatively, using reduction to characteristic p techniques …

It is proved that an excellent local ring of prime characteristic in which a single ideal
generated by any system of parameters is tightly closed must be pseudorational. A key point …

We generalize the notions of F-regular and F-pure rings to pairs (R,a^t) of rings R and ideals
a⊂R with real exponent t> 0, and investigate these properties. These “F-singularities of …