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Injective sheaf
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Mapping Functions and Surjections
Explores mapping functions, surjections, injective and surjective functions, and bijective functions.
Derived Functor Approach
Covers the derived functor approach to Čech cohomology, emphasizing the relationship between derived functors and sheaf theory.
Cohomology: Cross Product
Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Ringed Spaces: Definitions and Properties
Covers the definitions and properties of ringed spaces, including morphisms and examples of locally ringed spaces.
Primary Decomposition: Behaviour and Localisation
Explores primary decomposition, recovering rings from spectra, and studying regular functions on spectra.
Quasi-coherence 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.
Ample Invertible Sheaves
Introduces ample invertible sheaves and their properties in algebraic geometry.
Coherent Sheaves: Locally Ringed Space
Covers the definition of coherent sheaves and their properties in the context of algebraic geometry.
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Group Cohomology
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.