[图书][B] Cohen-macaulay representations
GJ Leuschke, R Wiegand - 2012 - books.google.com
This book is a comprehensive treatment of the representation theory of maximal Cohen-
Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative …
Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative …
F-signature exists
K Tucker - Inventiones mathematicae, 2012 - Springer
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∈ …
p> 0 and perfect residue field. Let R^1/p^e be the ring of pe-th roots of elements of R for e∈ …
Classifying thick subcategories of the stable category of Cohen–Macaulay modules
R Takahashi - Advances in Mathematics, 2010 - Elsevier
Various classification theorems of thick subcategories of a triangulated category have been
obtained in many areas of mathematics. In this paper, as a higher-dimensional version of the …
obtained in many areas of mathematics. In this paper, as a higher-dimensional version of the …
The F-signature and strong F-regularity
IM Aberbach, GJ Leuschke - arXiv preprint math/0208067, 2002 - arxiv.org
arXiv:math/0208067v2 [math.AC] 25 Nov 2002 Page 1 arXiv:math/0208067v2 [math.AC] 25
Nov 2002 THE F-SIGNATURE AND STRONG F-REGULARITY IAN M. ABERBACH AND …
Nov 2002 THE F-SIGNATURE AND STRONG F-REGULARITY IAN M. ABERBACH AND …
Quantifying singularities with differential operators
H Brenner, J Jeffries, L Núñez-Betancourt - Advances in Mathematics, 2019 - Elsevier
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 …
many interesting properties. For example, this invariant detects (non) singularity and strong …
[PDF][PDF] A survey of test ideals
K Schwede, K Tucker - Progress in commutative algebra, 2012 - library.oapen.org
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 …
theory of tight closure, and since their invention have been closely tied to the theory of …
F-signature and Hilbert–Kunz multiplicity: a combined approach and comparison
T Polstra, K Tucker - Algebra & Number Theory, 2018 - msp.org
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 …
related limits governed by Frobenius and Cartier linear actions in positive characteristic …
A guided tour to normalized volume
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 …
Guided Tour to Normalized Volume Chi Li, Yuchen Liu and Chenyang Xu Dedicated to Gang …
Perfectoid signature, perfectoid Hilbert-Kunz multiplicity, and an application to local fundamental groups
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 …
multiplicity by utilizing the perfectoidization functor of Bhatt-Scholze and Faltings' normalized …
Dominant local rings and subcategory classification
R Takahashi - International Mathematics Research Notices, 2023 - academic.oup.com
We introduce a new notion of commutative noetherian local rings, which we call dominant.
We explore fundamental properties of dominant local rings and compare them with other …
We explore fundamental properties of dominant local rings and compare them with other …