Math Notes

University Mathematics

Algebraic Geometry

Overview Concept Coherent and Quasi-coherent Sheaves Concept Sheaf Cohomology $H^i(X, \mathcal{F})$Concept Čech Cohomology Concept Ext Sheaves and Local-to-Global Spectral Sequence Concept The Dualizing Sheaf $\omega_X$Theorem Serre's Vanishing Theorem Theorem Serre Duality Theorem The Riemann–Roch Theorem Theorem Cohomology of Projective Space Proof Proof of Serre Duality

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Cohomology

Cohomology

Concepts

Coherent and Quasi-coherent Sheaves Sheaf Cohomology $H^i(X, \mathcal{F})$Čech Cohomology Ext Sheaves and Local-to-Global Spectral Sequence The Dualizing Sheaf $\omega_X$

Theorems

Serre's Vanishing Theorem Serre Duality The Riemann–Roch Theorem Cohomology of Projective Space

Proofs

Proof of Serre Duality

Mathematics Lecture Notes