Homological Questions In Local Algebra

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Homological Questions In Local Algebra

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Author : Jan R. Strooker
language : en
Publisher: Cambridge University Press
Release Date : 1990-09-06

Homological Questions In Local Algebra written by Jan R. Strooker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-09-06 with Mathematics categories.

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.

Topics In The Homological Theory Of Modules Over Commutative Rings

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Author : Melvin Hochster
language : en
Publisher: American Mathematical Soc.
Release Date : 1975-12-31

Topics In The Homological Theory Of Modules Over Commutative Rings written by Melvin Hochster and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-12-31 with Mathematics categories.

This volume contains expository lectures by Melvin Hochster from the CBMS Regional Conference in Mathematics held at the University of Nebraska, June 1974. The lectures deal mainly with recent developments and still open questions in the homological theory of modules over commutative (usually, Noetherian) rings. A good deal of attention is given to the role ``big'' Cohen-Macaulay modules play in clearing up some of the open questions. A modest knowledge of commutative rings and familarity with (the long exact sequences for) Tor and Ext should suffice as a background for the reader.

Completion Ech And Local Homology And Cohomology

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Author : Peter Schenzel
language : en
Publisher: Springer
Release Date : 2018-09-15

Completion Ech And Local Homology And Cohomology written by Peter Schenzel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-15 with Mathematics categories.

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.

Homological Algebra In Local Rings

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Author : Ann L. Burch
language : en
Publisher:
Release Date : 1967

Homological Algebra In Local Rings written by Ann L. Burch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.

Homological Algebra And Ring Theory

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Author : James Patrick Jans
language : en
Publisher:
Release Date : 1961

Homological Algebra And Ring Theory written by James Patrick Jans and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Algebra, Homological categories.

Relative Homological Algebra

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Author : Edgar E. Enochs
language : en
Publisher: Walter de Gruyter
Release Date : 2011-10-27

Relative Homological Algebra written by Edgar E. Enochs and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-27 with Mathematics categories.

This is the second revised edition of an introduction to contemporary relative homological algebra. It supplies important material essential to understand topics in algebra, algebraic geometry and algebraic topology. Each section comes with exercises providing practice problems for students as well as additional important results for specialists. In this new edition the authors have added well-known additional material in the first three chapters, and added new material that was not available at the time the original edition was published. In particular, the major changes are the following: Chapter 1: Section 1.2 has been rewritten to clarify basic notions for the beginner, and this has necessitated a new Section 1.3. Chapter 3: The classic work of D. G. Northcott on injective envelopes and inverse polynomials is finally included. This provides additional examples for the reader. Chapter 11: Section 11.9 on Kaplansky classes makes volume one more up to date. The material in this section was not available at the time the first edition was published. The authors also have clarified some text throughout the book and updated the bibliography by adding new references. The book is also suitable for an introductory course in commutative and ordinary homological algebra.

Local Algebra

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Author : Jean-Pierre Serre
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Local Algebra written by Jean-Pierre Serre and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Some Homological Results In Commutative Algebra

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Author : Leah Helene Gold
language : en
Publisher:
Release Date : 2002

Some Homological Results In Commutative Algebra written by Leah Helene Gold and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.

Local Fields

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Author : Jean-Pierre Serre
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Local Fields written by Jean-Pierre Serre and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray.

Arithmetic Of Blowup Algebras

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Author : Wolmer V. Vasconcelos
language : en
Publisher: Cambridge University Press
Release Date : 1994-02-25

Arithmetic Of Blowup Algebras written by Wolmer V. Vasconcelos and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-25 with Mathematics categories.

This book discusses recent developments in an important area of computational commutative algebra.