Vector Bundles & Locally Free Sheaves

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

Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.

Introduces ample invertible sheaves and their properties in algebraic geometry.

Covers the concept of quasi-coherence in algebraic geometry, discussing the lifting of functions, sections of sheaves, and push forwards of coherent sheaves.

Primary Decomposition: Behaviour and Localisation

Explores primary decomposition, recovering rings from spectra, and studying regular functions on spectra.