Completion Ech And Local Homology And Cohomology
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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.
Algebraic Topology
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Author : Andrew H. Wallace
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01
Algebraic Topology written by Andrew H. Wallace and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
Surveys several algebraic invariants, including the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.
Local Cohomology
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Author : Alexander Grothendieck
language : en
Publisher:
Release Date : 1967
Local Cohomology written by Alexander Grothendieck 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.
Homology And Cohomology Theory
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Author : William S. Massey
language : en
Publisher:
Release Date : 1978
Homology And Cohomology Theory written by William S. Massey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
Local Cohomology
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Author : Robin Hartshorne
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1967
Local Cohomology written by Robin Hartshorne and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Mathematics categories.
Traces Of Differential Forms And Hochschild Homology
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Author : Reinhold Hübl
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1989-03-22
Traces Of Differential Forms And Hochschild Homology written by Reinhold Hübl and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-03-22 with Mathematics categories.
This monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms. The approach uses Hochschild-homology, the definition of which is extended to the category of topological algebras. Many results for Hochschild-homology of commutative algebras also hold for Hochschild-homology of topological algebras. In particular, after introducing an appropriate notion of completion of differential algebras, one gets a natural transformation between differential forms and Hochschild-homology of topological algebras. Traces of differential forms are of interest to everyone working with duality theory and residue symbols. Hochschild-homology is a useful tool in many areas of k-theory. The treatment is fairly elementary and requires only little knowledge in commutative algebra and algebraic geometry.
Equivariant Homotopy And Cohomology Theory
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Author : J. Peter May
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Equivariant Homotopy And Cohomology Theory written by J. Peter May 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 1996 with Homology theory categories.
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.
Local Cohomology
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Author : Robin Hartshorne
language : en
Publisher:
Release Date : 2014-01-15
Local Cohomology written by Robin Hartshorne and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Local Cohomology
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Author : A. Grothendieck
language : en
Publisher:
Release Date : 1967
Local Cohomology written by A. Grothendieck and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Algebra, Homological categories.
Lecture Notes In Algebraic Topology
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Author : James F. Davis
language : en
Publisher: American Mathematical Society
Release Date : 2023-05-22
Lecture Notes In Algebraic Topology written by James F. Davis and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-22 with Mathematics categories.
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.