Lecture

Homological Algebra: Basics and Applications

Related lectures (32)

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Acyclic Models: Cup Product and Cohomology

Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.

Algebraic Kunneth Theorem

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Cohomology: Cross Product

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Cohomology Real Projective Space

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

Curl and Exact Sequences

Covers the concept of curl in vector calculus and De Rham cohomology.

Injective Modules: Ox-Modules and Injectives

Covers injective modules, Ox-modules, and their relevance in algebraic structures, emphasizing their importance in resolving acyclic resolutions and computing cohomology.

Cohomology Groups: Hopf Formula

Explores the Hopf formula in cohomology groups, emphasizing the 4-term exact sequence and its implications.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Long Exact Sequence of Ext-Modules

Explores the long exact sequence of Ext-modules and their computations in homological algebra.

Topology of Adeles

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, including path object construction and fibrations.

Derived Functor Approach

Covers the derived functor approach to Čech cohomology, emphasizing the relationship between derived functors and sheaf theory.

Finite Abelian Groups: Classification Theorem

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

Cohomology: Recollection and Foliations

Covers cohomology, injective resolutions, and acyclic objects in an abelian category.

Coherent Sheaves: Locally Ringed Space

Covers the definition of coherent sheaves and their properties in the context of algebraic geometry.

Algebraic Cycles and Etale Cohomology

Explores algebraic cycles, etale cohomology, and counterexamples to the Hodge conjecture.

Topology Seminar: Tower Sequences and Homomorphisms

Explores tower sequences, homomorphisms, and their applications in topology, including the computation of homology and the construction of telescopes.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Cohomology of Quasi-Coherent on Affine Schemes

Covers the cohomology of quasi-coherent sheaves on affine schemes.