Algebra 3: homological algebra and its applications
by Lal, Ramji
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…
Read More ↓Title Statements
- Full title :Algebra 3 : homological algebra and its applications / Ramji Lal.
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.
Read More ↓Edition Statements
- Publication Date:©2021
Publication Statements
- Publisher(s):Springer
- Place of Publication:Singapore
- Language:eng
- Publication Date:©2021
The Physical Object
- Description:xv, 300 pages ; : 24 cm.
Edition Identifiers
- ISBN:9813363258, 9789813363250
- oclc:on1225621456
- LC Classification:QA169
- Dewey Decimal:514.2
Table of 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
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