Algebra 3

1. Front Matter

   Pages i-xv

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2. Homological Algebra 1

   • Ramji Lal

   Pages 1-67

3. Homological Algebra 2, Derived Functors

   • Ramji Lal

   Pages 69-138

4. Homological Algebra 3: Examples and Applications

   • Ramji Lal

   Pages 139-210

5. Sheaf Co-homology and Its Applications

   • Ramji Lal

   Pages 211-293

6. Back Matter

   Pages 295-300

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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.

• Homological algebra
• Commutative algebra
• Algebraic geometry
• Algebraic curves
• semi-simple lie algebra
• Chevalley groups

“This is an excellent book on Homological Algebra. All topics dealt here are presented in a very
systematic way. It is an ideal handbook for any person desirous of pursuing research in Homological Algebra. … At the end of each section of each chapter an exhaustive list of exercises is given.” (Veereshwar A. Hiremath, zbMATH 1474.01001, 2021)

• University of Allahabad, Prayagraj, India

  Ramji Lal

Ramji Lal is a former professor and head of the Department of Mathematics at the University of Allahabad, India. He is also a former adjunct professor of the Harish-Chandra Research Institute (HRI), Allahabad, India. He started his research career at the Tata Institute of Fundamental Research (TIFR), Mumbai, and served the University of Allahabad in different capacities for over 43 years: as a professor, head of the department and the coordinator of the DSA program. At HRI, he initiated a postgraduate (PG) program in mathematics and coordinated the Nurture Program of National Board for Higher Mathematics (NBHM) from 1996 to 2000. After his retirement from the University of Allahabad, he had been the advisor cum adjunct professor at the Indian Institute of Information Technology (IIIT), Allahabad, for over three years. His research interests include group theory, algebraic K-theory and representation theory.

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