Homological Invariants of Modules Over Commutative Rings
Author : Paul Roberts
Publisher :
Page : 122 pages
File Size : 45,15 MB
Release : 1980
Category : Commutative rings
ISBN :
Topics in the Homological Theory of Modules Over Commutative Rings
Author : Melvin Hochster
Publisher : American Mathematical Soc.
Page : 86 pages
File Size : 10,21 MB
Release : 1975
Category : Mathematics
ISBN : 0821816748
Book Description
Contains expository lectures from the CBMS Regional Conference in Mathematics held at the University of Nebraska, June 1974. This book deals mainly with developments and still open questions in the homological theory of modules over commutative (usually, Noetherian) rings.
Six Lectures on Commutative Algebra
Author : J. Elias
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 19,86 MB
Release : 2010-03-17
Category : Mathematics
ISBN : 3034603290
Book Description
Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume is a synthesis of the lectures given by these authors. Research workers as well as graduate students in commutative algebra and nearby areas will find a useful overview of the field and recent developments in it. Reviews "All six articles are at a very high level; they provide a thorough survey of results and methods in their subject areas, illustrated with algebraic or geometric examples." - Acta Scientiarum Mathematicarum Avramov lecture: "... it contains all the major results [on infinite free resolutions], it explains carefully all the different techniques that apply, it provides complete proofs (...). This will be extremely helpful for the novice as well as the experienced." - Mathematical reviews Huneke lecture: "The topic is tight closure, a theory developed by M. Hochster and the author which has in a short time proved to be a useful and powerful tool. (...) The paper is extremely well organized, written, and motivated." - Zentralblatt MATH Schenzel lecture: "... this paper is an excellent introduction to applications of local cohomology." - Zentralblatt MATH Valla lecture: "... since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory." - Mathematical reviews Vasconcelos lecture: "This is a very useful survey on invariants of modules over noetherian rings, relations between them, and how to compute them." - Zentralblatt MATH
Completion, Čech and Local Homology and Cohomology
Author : Peter Schenzel
Publisher : Springer
Page : 352 pages
File Size : 26,68 MB
Release : 2018-09-15
Category : Mathematics
ISBN : 3319965174
Book Description
The aim of the present monograph is a thorough study of the adic-completion, its left derived functors and their relations to the local cohomology functors, as well as several completeness criteria, related questions and various dualities formulas. A basic construction is the Čech complex with respect to a system of elements and its free resolution. The study of its homology and cohomology will play a crucial role in order to understand left derived functors of completion and right derived functors of torsion. This is useful for the extension and refinement of results known for modules to unbounded complexes in the more general setting of not necessarily Noetherian rings. The book is divided into three parts. The first one is devoted to modules, where the adic-completion functor is presented in full details with generalizations of some previous completeness criteria for modules. Part II is devoted to the study of complexes. Part III is mainly concerned with duality, starting with those between completion and torsion and leading to new aspects of various dualizing complexes. The Appendix covers various additional and complementary aspects of the previous investigations and also provides examples showing the necessity of the assumptions. The book is directed to readers interested in recent progress in Homological and Commutative Algebra. Necessary prerequisites include some knowledge of Commutative Algebra and a familiarity with basic Homological Algebra. The book could be used as base for seminars with graduate students interested in Homological Algebra with a view towards recent research.
Twenty-Four Hours of Local Cohomology
Author : Srikanth B. Iyengar
Publisher : American Mathematical Society
Page : 108 pages
File Size : 30,26 MB
Release : 2022-07-19
Category : Mathematics
ISBN : 1470471590
Book Description
This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Gröbner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.
Commutative Ring Theory
Author : Hideyuki Matsumura
Publisher : Cambridge University Press
Page : 338 pages
File Size : 31,91 MB
Release : 1989-05-25
Category : Mathematics
ISBN : 9780521367646
Book Description
This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Algebra
Author : I. Martin Isaacs
Publisher : American Mathematical Soc.
Page : 531 pages
File Size : 20,35 MB
Release : 2009
Category : Mathematics
ISBN : 0821847996
Book Description
as a student." --Book Jacket.
Homological Questions in Local Algebra
Author : Jan R. Strooker
Publisher : Cambridge University Press
Page : 325 pages
File Size : 45,69 MB
Release : 1990-09-06
Category : Mathematics
ISBN : 0521315263
Book Description
This book presents an account of several conjectures arising in commutative algebra from the pioneering work of Serre and Auslander-Buchsbaum. The approach is via Hochster's 'Big Cohen-Macaulay modules', though the complementary view point of Peskine-Szpiro and Roberts, who study the homology of certain complexes, is not neglected. Various refinements of Hochster's construction, obtained in collaboration with Bartijn, are included. A special feature is a long chapter written by Van den Dries which explains how a certain type of result can be 'lifted' from prime characteristic to characteristic zero. Though this is primarily a research monograph, it does provide introductions to most of the topics treated. Non-experts may therefore find it an appealing guide into an active area of algebra.
Commutative Algebra
Author : David Eisenbud
Publisher : Springer Science & Business Media
Page : 784 pages
File Size : 18,71 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461253500
Book Description
This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
Local Algebra
Author : Jean-Pierre Serre
Publisher : Springer Science & Business Media
Page : 139 pages
File Size : 12,27 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3662042037
Book Description
This is an English translation of the now classic "Algbre Locale - Multiplicits" originally published by Springer as LNM 11. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities. Many modifications to the original French text have been made for this English edition, making the text easier to read, without changing its intended informal character.
