606 Algebraic Geometry

• Gilbert Basis And Noether Normalization
• Nullstellensatz And Corollary
• Zariski Topology
• Extending Nullstellensatz
• Untitled
• Category Of Affine Varieties
• Equivalence Of Affine Varieties And k-Algebras
• Spec
• Topology Of Spec
• Category Theory Review
• Presheaves And Sheaves
• Local Ringed Space
• Affine Schemes
• Morphisms Of (Pre) Sheaves
• Sheafification
• Push forward And Pullback
• Equivalence Of Ring And Affine Scheme
• Remarks About The Equivalence
• Adjoint Functors
• Spec And Global Sections Are Adjoint
• Remarks On Global Sections
• Open Scheme And Gluing
• Fiber Product Of Schemes
• Separated And Reduced Schemes
• Varieties As Schemes
• Fiber Of A Map
• Base Change
• Integral Scheme
• Dimension Of Scheme
• Locally Noetherian Schemes
• More Noetherian Schemes
• Graded Rings And Proj
• Projective Space Over A Ring
• T Points Of A Scheme
• Yoneda Lemma
• Separated Schemes
• Valuation Criterion
• Using Valuation Criterion To Show Projective Is Proper
• Projective Space Is Separated
• Cancellation Properties
• Projective Maps Are Nice
• O_x Modules
• Associating An O_x Module To A Module
• Affine O_x Modules
• Gluing Modules
• Quasi Coherence And Exactness
• Stability Of Quasi Coherence
• Quasi Separated
• Push forward Of Quasi Coherent Sheaves
• Quasi Affine
• Sheaf Of Ideals Cutting Out Y
• Affine Morphisms And Quasi Coherent O_x Modules
• Vector Bundle To A Sheaf
• Spec Of Sheaf Of O_S Modules
• Group Schemes
• Twists And Proj
• Ample And Very Ample Line Bundles
• Relationship Between Ample And Global Sections
• Quasi Projective Maps
• Picard Groups
• Untitled
• Untitled
• Degree Of Divisors
• Class Groups And Subsets
• Cartier Class Group
• Relationship Between CaCl And Pic
• Nonsingular And Rank Of Jacobian
• Flat Maps
• Kaler Differentials
• O Smooth/Unramified/Etale
• Nonsingular Locus Is Dense
• Sheafs Of Differentials
• Criteria For Regularity
• Smooth And Etale Morphisms
• Smooth Is Formally Smooth
• Chek? Cohomology
• Ample Revisited
• Another Ample Definition
• Ample Bundles And Quasi Projective
• Untitled
• Grassmanian Sheaves
• More Grassmanians
• Abelian Category
• Exact Sequences
• Enough Injectives
• Sheaves Are Abelian
• Right Derived Functors
• Untitled
• Abstract DeRahm Theorem
• Other Cohomology Theories
• Flasque Resolutions
• Check Cohomology
• Check Cohomology