Homological Algebra: Basics and Applications

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Related lectures (36)

Finite Abelian Groups: Classification Theorem Log in to Mediaspace to watch this video

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

Cohomology: Recollection and Foliations Log in to Mediaspace to watch this video

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

Algebraic Cycles and Etale Cohomology Log in to Mediaspace to watch this video

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

Cohomology of Quasi-Coherent on Affine Schemes Log in to Mediaspace to watch this video

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

Homology of Projective Space Log in to Mediaspace to watch this video

Covers the homology of projective space, focusing on cohomology and exact sequences.

Universal Coefficient Theorems Log in to Mediaspace to watch this video

Delves into the universal coefficient theorems in homological algebra, showcasing their practical application in computing homology and cohomology groups.

Decomposition of Group Algebras Log in to Mediaspace to watch this video

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Coherent Sheaves: Locally Ringed Space Log in to Mediaspace to watch this video

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

Ample Invertible Sheaves Log in to Mediaspace to watch this video

Introduces ample invertible sheaves and their properties in algebraic geometry.

Ideals and Representations Log in to Mediaspace to watch this video

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Algebraic Geometry: Forms and Maps Log in to Mediaspace to watch this video

Covers the concept of forms in algebraic geometry and the implications of constructing Bloch(A) from glued copies of A.

Regularity and Noetherian Local Rings Log in to Mediaspace to watch this video

Covers the concepts of regularity and Noetherian local rings in algebraic structures.

Homogeneous Ideals and Regular Rings Log in to Mediaspace to watch this video

Explores homogeneous ideals, regular rings, N-graded rings, and closed sets in projective geometry.

Dedekind Rings: Integral Extensions and Noetherian Rings Log in to Mediaspace to watch this video

Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.

The Quadratic Linking Degree Log in to Mediaspace to watch this video

Introduces the quadratic linking degree in motivic knot theory, covering knot theory basics, algebraic geometry, and intersection theory.

Algebraic Structures: Small Order Groups Log in to Mediaspace to watch this video

Explores small order groups, group morphisms, and the second isomorphism theorem.

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