Homological algebra - учебный курс | ИСТИНА – Интеллектуальная Система Тематического Исследования НАукометрических данных

Автор: Панов Тарас Евгеньевич
Год создания: 2023
Организация: МГУ имени М.В. Ломоносова
Курс на иностранном языке
Описание: Семестровый курс по гомологической алгебре, читаемый в рамках магистерской программы "Geometry and Quantum Fields" (2-й год) в Институте Теоретической и Математической Физики, МГУ. Annotation: 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). Course plan: 1. Algebras and modules, chain complexes, differential graded algebras, homology. 2. Chain homotopies, quasi-isomorphisms, long exact sequences. 3. Free, projective and injective modules, resolutions. 4. Tor and Ext. 5. Examples of resolutions: minimal resolution of graded modules, Koszul resolution, bar an cobar constructions. 6. Systems of parameters, regular sequences and Cohen–Macaulay algebras. 7. Projective dimension and depth of modules. 8. Multiplications: Eilenberg–Zilber and Kuenneth theorems. 9. Formality and Massey products. 10. Spectral sequences of a filtered complex and bicomplex. 10. A∞-morphisms, extended functoriality of Tor, the Eilenberg– Moore spectral sequence.
Добавил в систему: Панов Тарас Евгеньевич

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Homological algebraучебный курс

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