Vector Bundles & Locally Free Sheaves

Related lectures (32)

Page 3 of 4

Explores regularity in algebraic geometry and the geometric implications of the Jacobian criterion.

Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.

Covers the concept of sheaves, emphasizing the unique determination of functions by local data and the importance of direct limits.

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

Covers modern algebraic geometry, focusing on schemes and affine schemes, including a review of classical algebraic geometry and Bézout's theorem.

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

Covers the definitions and properties of ringed spaces, including morphisms and examples of locally ringed spaces.

Covers free resolution of modules and projective modules in module theory.

Covers the concept of locally Noetherian schemes in algebraic geometry.

Covers the Weil conjectures on rationality, functional equation, and the Riemann hypothesis, exploring properties of varieties in algebraic geometry.