In the last two decades Cohen-Macaulay rings and modules have been central topics in
commutative algebra. This book meets the need for a thorough, self-contained introduction …

This paper contains two theorems concerning the theory of maximal Cohen–Macaulay
modules. The first theorem proves that certain Ext groups between maximal Cohen …

In this paper we generalize standard results about non-commutative resolutions of quotient
singularities for finite groups to arbitrary reductive groups. We show in particular that …

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∈ …

A smooth projective variety is said to be Fano if its anti-canonical bundle is ample. The
Kodaira vanishing theorem easily implies vanishing of all higher cohomology modules of …

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 …

It is shown that the tight closure of a submodule in a Artinian module is the same as its
finitistic tight closure, when the modules are graded over a finitely generated [inline-graphic …

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 …

A Guided Tour to Normalized Volume Page 1 Progress in Mathematics, Vol. 333, 167–219 A
Guided Tour to Normalized Volume Chi Li, Yuchen Liu and Chenyang Xu Dedicated to Gang …