Title:
Algebra 3 : homological algebra and its applications / Ramji Lal.
Infosys Science Foundation series
Infosys Science Foundation Series.
Author:
Lal, Ramji, author.
General Notes:
Includes bibliographical references and index.
Intro -- Preface -- Contents -- About the Author -- Notations -- 1 Homological Algebra 1 -- 1.1 Categories and Functors -- 1.2 Abelian Categories -- 1.3 Category of Chain Complexes and Homology -- 1.4 Extensions and the Functor EXT -- 2 Homological Algebra 2, Derived Functors -- 2.1 Resolutions and Extensions -- 2.2 Tensor and Tor Functors -- 2.3 Abstract Theory of Derived Functors -- 2.4 Kunneth Formula -- 2.5 Spectral Sequences -- 3 Homological Algebra 3: Examples and Applications -- 3.1 Polyhedrons and Simplicial Homology -- 3.2 Applications -- 3.3 Co-homology of Groups
3.4 Calculus and Co-homology -- 4 Sheaf Co-homology and Its Applications -- 4.1 Presheaves and Sheaves -- 4.2 Sheaf Co-homology and ech Co-homology -- 4.3 Algebraic Varieties -- 4.4 Schemes -- 4.5 Weil Conjectures and l-adic Co-homology -- Appendix Bibliography -- Index
This book, the third book in the four-volume series in algebra, deals with important topics in homological algebra, including abstract theory of derived functors, sheaf co-homology, and an introduction to etale and l-adic co-homology. It contains four chapters which discuss homology theory in an abelian category together with some important and fundamental applications in geometry, topology, algebraic geometry (including basics in abstract algebraic geometry), and group theory. The book will be of value to graduate and higher undergraduate students specializing in any branch of mathematics. The author has tried to make the book self-contained by introducing relevant concepts and results required. Prerequisite knowledge of the basics of algebra, linear algebra, topology, and calculus of several variables will be useful.
Online resource; title from PDF title page (SpringerLink, viewed March 25, 2021).
Publisher:
Springer,
Publication Place:
Singapore :
ISBN:
9789813363267
9813363266
9789813363274
9813363274
9789813363281
9813363282
9813363258
9789813363250
Subject:
Algebra, Homological.
Algebra, Homological.
�Algebra homol�ogica.
Series:
Infosys Science Foundation series
Infosys Science Foundation Series.
Contents:
Intro -- Preface -- Contents -- About the Author -- Notations -- 1 Homological Algebra 1 -- 1.1 Categories and Functors -- 1.2 Abelian Categories -- 1.3 Category of Chain Complexes and Homology -- 1.4 Extensions and the Functor EXT -- 2 Homological Algebra 2, Derived Functors -- 2.1 Resolutions and Extensions -- 2.2 Tensor and Tor Functors -- 2.3 Abstract Theory of Derived Functors -- 2.4 Kunneth Formula -- 2.5 Spectral Sequences -- 3 Homological Algebra 3: Examples and Applications -- 3.1 Polyhedrons and Simplicial Homology -- 3.2 Applications -- 3.3 Co-homology of Groups
3.4 Calculus and Co-homology -- 4 Sheaf Co-homology and Its Applications -- 4.1 Presheaves and Sheaves -- 4.2 Sheaf Co-homology and ech Co-homology -- 4.3 Algebraic Varieties -- 4.4 Schemes -- 4.5 Weil Conjectures and l-adic Co-homology -- Appendix Bibliography -- Index
Electronic Location:
https://doi.org/10.1007/978-981-33-6326-7
http://public.eblib.com/choice/PublicFullRecord.aspx?p=6510185
http://link.springer.com/10.1007/978-981-33-6326-7
https://link.springer.com/10.1007/978-981-33-6326-7
https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=2802602
Publication Date:
[2021]
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