Suppose R is ad-dimensional reduced F-finite Noetherian local ring with prime characteristic
p> 0 and perfect residue field. Let R^1/p^e be the ring of pe-th roots of elements of R for e∈ …

The F-signature of a local ring of prime characteristic is a numerical invariant that detects
many interesting properties. For example, this invariant detects (non) singularity and strong …

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 present a unified approach to the study of F-signature, Hilbert–Kunz multiplicity, and
related limits governed by Frobenius and Cartier linear actions in positive characteristic …

We define a (perfectoid) mixed characteristic version of $ F $-signature and Hilbert-Kunz
multiplicity by utilizing the perfectoidization functor of Bhatt-Scholze and Faltings' normalized …

For a reduced F-finite ring R of characteristic p> 0 and q= pe one can write where M q has
no free direct summands over R. We investigate the structure of F-finite, F-pure rings R by …

We prove that the local etale fundamental group of a strongly $ F $-regular singularity is
finite (and likewise for the\'etale fundamental group of the complement of a codimension …

Let (R, m, k) be a d-dimensional Noetherian reduced local ring of prime characteristic p such
that [Formula: see text] are finite over R for all e∈ N (ie R is F-finite). Consider the sequence …

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 …

In this paper we ask the following question: What is the minimal value of the difference $\ehk
(I)-\ehk (I') $ for ideals $ I'\supseteq I $ with $ l_A (I'/I)= 1$? In order to answer to this …