Completion Čech And Local Homology And Cohomology

Author : Peter Schenzel,Anne-Marie Simon
Publisher : Springer
Page : 346 pages
File Size : 41,8 Mb
Release : 2018-09-15
Category : Mathematics
ISBN : 9783319965178

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Completion, Čech and Local Homology and Cohomology by Peter Schenzel,Anne-Marie Simon Pdf

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.

Author : J. Peter May,M. Cole
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 55,6 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821803196

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Equivariant Homotopy and Cohomology Theory by J. Peter May,M. Cole Pdf

This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.

Author : Gennady Lybeznik
Publisher : CRC Press
Page : 366 pages
File Size : 55,9 Mb
Release : 2001-10-18
Category : Mathematics
ISBN : 0824707419

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Local Cohomology and Its Applications by Gennady Lybeznik Pdf

This volume collects presentations from the international workshop on local cohomology held in Guanajuato, Mexico, including expanded lecture notes of two minicourses on applications in equivariant topology and foundations of duality theory, and chapters on finiteness properties, D-modules, monomial ideals, combinatorial analysis, and related topics. Featuring selected papers from renowned experts around the world, Local Cohomology and Its Applications is a provocative reference for algebraists, topologists, and upper-level undergraduate and graduate students in these disciplines.

Author : Irena Peeva
Publisher : Springer Nature
Page : 898 pages
File Size : 46,5 Mb
Release : 2022-02-18
Category : Mathematics
ISBN : 9783030896942

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Commutative Algebra by Irena Peeva Pdf

This contributed volume is a follow-up to the 2013 volume of the same title, published in honor of noted Algebraist David Eisenbud's 65th birthday. It brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Category Theory, Combinatorics, Computational Algebra, Homological Algebra, Hyperplane Arrangements, and Non-commutative Algebra. The book aims to showcase the area and aid junior mathematicians and researchers who are new to the field in broadening their background and gaining a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.

Author : I.M. James
Publisher : Elsevier
Page : 1336 pages
File Size : 51,6 Mb
Release : 1995-07-18
Category : Mathematics
ISBN : 9780080532981

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Handbook of Algebraic Topology by I.M. James Pdf

Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.

Author : Summer School on Interactions between Homotopy Theory and Algebra
Publisher : American Mathematical Soc.
Page : 352 pages
File Size : 50,7 Mb
Release : 2007
Category : Commutative algebra
ISBN : 9780821838143

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Interactions between Homotopy Theory and Algebra by Summer School on Interactions between Homotopy Theory and Algebra Pdf

This book is based on talks presented at the Summer School on Interactions between Homotopy theory and Algebra held at the University of Chicago in the summer of 2004. The goal of this book is to create a resource for background and for current directions of research related to deep connections between homotopy theory and algebra, including algebraic geometry, commutative algebra, and representation theory. The articles in this book are aimed at the audience of beginning researchers with varied mathematical backgrounds and have been written with both the quality of exposition and the accessibility to novices in mind.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 743 pages
File Size : 55,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9789400903654

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Author : National Science Foundation (U.S.)
Publisher : Unknown
Page : 728 pages
File Size : 52,8 Mb
Release : 2024-07-01
Category : Engineering
ISBN : STANFORD:36105029358855

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Summaries of Projects Completed by National Science Foundation (U.S.) Pdf

Author : Anonim
Publisher : Unknown
Page : 752 pages
File Size : 42,5 Mb
Release : 2024-07-01
Category : Engineering
ISBN : UOM:39015081530670

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Summaries of Projects Completed in Fiscal Year ... by Anonim Pdf

Author : Alexander Grothendieck
Publisher : Unknown
Page : 106 pages
File Size : 46,7 Mb
Release : 1967
Category : Electronic
ISBN : OCLC:63443100

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Local Cohomology by Alexander Grothendieck Pdf

Author : Anonim
Publisher : Unknown
Page : 626 pages
File Size : 40,9 Mb
Release : 1974
Category : Mathematics
ISBN : UOM:39015026008717

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Revue Roumaine de Mathématiques Pures Et Appliquées by Anonim Pdf

Author : David E. Dobbs
Publisher : Unknown
Page : 194 pages
File Size : 54,7 Mb
Release : 1970
Category : Mathematics
ISBN : STANFORD:36105002010283

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Cech Cohomological Dimensions for Commutative Rings by David E. Dobbs Pdf

The four chapters comprising this volume are concerned with attaching dimensions to commutative rings by means of Cech cohomology and comparing the results to those obtained using Grothendieck cohomology.

Author : Ulrich Görtz,Torsten Wedhorn
Publisher : Springer Nature
Page : 877 pages
File Size : 50,6 Mb
Release : 2023-11-22
Category : Mathematics
ISBN : 9783658430313

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Algebraic Geometry II: Cohomology of Schemes by Ulrich Görtz,Torsten Wedhorn Pdf

This book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume Algebraic Geometry I: Schemes. It begins by discussing in detail the notions of smooth, unramified and étale morphisms including the étale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck's algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously. The text contains many exercises that allow the reader to check their comprehension of the text, present further examples or give an outlook on further results.

Author : Robin Hartshorne,Alexandre Grothendieck
Publisher : Unknown
Page : 128 pages
File Size : 50,8 Mb
Release : 1967
Category : Algebra, Homological
ISBN : STANFORD:36105031722437

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Local Cohomology by Robin Hartshorne,Alexandre Grothendieck Pdf

Author : M. P. Brodmann,R. Y. Sharp
Publisher : Cambridge University Press
Page : 514 pages
File Size : 43,8 Mb
Release : 2013
Category : Mathematics
ISBN : 9780521513630

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Local Cohomology by M. P. Brodmann,R. Y. Sharp Pdf

On its original publication, this algebraic introduction to Grothendieck's local cohomology theory was the first book devoted solely to the topic and it has since become the standard reference for graduate students. This second edition has been thoroughly revised and updated to incorporate recent developments in the field.