Homological Algebra
Математика
28 лекций
https://itmp.msu.ru/en/mscgeom...
A semester course introducing the basic constructions and techniques of homological algebra used in algebraic topology, algebraic geometry, and forming the basis of a number of geometric methods in mathematical physics.
The topics covered include chain complexes and differential graded al- gebras, quasi-isomorphisms, projective and injective modules, resolu- tions, homological dimension, Tor and Ext functors, regular sequences and Cohen–Macaulay rings, bicomplexes and filtered complexes, spec- tral sequences, A∞-morphisms.
Prerequisites: a basic course in algebra (groups, rings, modules, vector spaces), basic concepts of topology (continuous maps, homotopy).
2025
лекции
Математика
Преподаватель
- 01:27:52Lecture 1. Introduction to Homological Algebra
- 01:27:55Lecture 2. Projective and Injective Modules
- 01:36:46Lecture 3. Exercises on Projective and Injective Modules
- 58:07Lecture 4. Tor and Ext Functors
- 01:26:51Lecture 5. Exercises on Tor and Ext
- 01:22:55Lecture 6. Flat Modules
- 01:30:56Lecture 7. Further Exercises on Ext
- 01:49:36Lecture 8. Spectral Sequences
- 01:21:49Lecture 9. Chain Complex Exercises
- 01:20:00Lecture 10. Kunneth Spectral Sequence
- 01:30:50Lecture 11. Serre Spectral Sequence
- 01:18:06Lecture 12. Zeeman Comparison Theorem
- 01:32:03Lecture 13. Spectral Sequences II
- 01:16:06Lecture 14. Graded Algebras
- 01:29:23Lecture 15. Projective Dimension. Introduction
- 01:12:49Lecture 16. Koszul Resolutions
- 01:26:49Lecture 17. Associated Prime Ideals
- 01:26:54Лекция 18. Auslander-Buchsbaum Theorem
- 01:11:11Lecture 19. Massey Products
- 01:31:33Lecture 20. Differential Graded Resolutions and Bar Resolution
- 01:22:09Lecture 21. Eilenberg–Moore Spectral Sequence
- 01:31:44Lecture 22. Eilenberg–Moore Spectral Sequence II
- 01:25:42Lecture 23. Group (Co)homology
- 01:11:23Lecture 24. Group (Co)homology II
- 01:49:46Lecture 25. Lyndon–Hochschild–Serre spectral sequence
- 58:31Lecture 26. Lie Algebra (Co)homology
- 02:35:42Lecture 27. Chevalley–Eilenberg Complex. Applications to Semisimple Lie Algebras
- 02:17:29Lecture 28. Hochschild (Co)homology. Hochschild-Kostant-Rosenberg Theorem