Vector Bundles & Locally Free Sheaves

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Related lectures (32)

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Homological Algebra: Basics and Applications

Covers the basics of Homological algebra, focusing on Ext modules and their significance in modern mathematics.

Cohomology of Quasi-Coherent on Affine Schemes

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

Group Cohomology

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

Modern Algebraic Geometry

Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.

Sheaf Morphisms and Localization

Explores F-G sheaf morphisms, sheafification, and localization in ring theory.

Algebraic Geometry: Localization and Prime Ideals

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

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.

Varieties with nef anti-canonical: Surjective Albanese

Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.

Algebraic Kunneth Theorem

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

Applications of Serre Duality

Explores the applications of Serre duality in Enriques-Severi-Zariski lemma, foliations, and Riemann-Roch theorem.