Algebra 3 : homological algebra and its applications / Ramji Lal.
Lal, Ramji, author.
2021
QA169
Available Online

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Title
Algebra 3 : homological algebra and its applications / Ramji Lal.
Author
Lal, Ramji, author.
ISBN
9789813363267 (electronic bk.)
9813363266 (electronic bk.)
9789813363274 (print)
9813363274
9789813363281 (print)
9813363282
9813363258
9789813363250
DOI
https://doi.org/10.1007/978-981-33-6326-7
Published
Singapore : Springer, [2021]
Language
English
Description
1 online resource
Item Number
10.1007/978-981-33-6326-7 doi
Call Number
QA169
Dewey Decimal Classification
512/.55
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file
PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed March 25, 2021).
Series
Infosys Science Foundation series.
Available in Other Form
Print version: 9789813363250
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Online Access
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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

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