Algebraic Geometry Summer 2020
52520.mp4Lecture 1: 5/25/20
Topics: Motivation for affine schemes, the Zariski topology on Spec(A), topological properties of Spec(A).
The introduction is from Geometry of Schemes by Eisenbud & Harris.
52820.mp4Lecture 2: 5/28/20
Topics: Topological properties of Spec(A), motivation for sheaves.
6120.mp4Lecture 3: 6/1/20
Topics: Sheaves, abelian categories.
6420.mp4Lecture 4: 6/4/20
Topics: Closed/ open immersions of locally ringed spaces, affine scheme
6820.mp4Lecture 5: 6/8/20
Topics: Schemes, morphism of schemes, equivalence of categories
61120.mp4Lecture 6: 6/11/20
Topics: Projective space
61520.mp4Lecture 7: 6/15/20
Topics: Noetherian schemes, reduced, irreducible, and integral schemes.
61820.mp4Lecture 8: 6/18/20
Topics: Algebraic varieties, dimension.
62220.mp4Lecture 9: 6/22/20
Topics: Dimension in the noetherian case, fibered products
62520.mp4Lecture 10: 6/25/20
Topics: Base change, fibers, reasonable properties of morphisms
62920.mp4Lecture 11: 6/29/20
Topics: Finiteness properties of morphisms, "geometric" properties
7220.mp4Lecture 12: 7/2/20
Topics: Quasi-finite morphism, Frobenius, separated morphism.
7620.mp4Lecture 13: 7/6/20
Topics: Proper morphisms
7920.mp4Lecture 14: 7/9/20
Topics: Projective morphisms, normal schemes
71320.mp4Lecture 15: 7/13/20
Topics: Normalization, Zariski tanget space
71520.mp4Lecture 16: 7/15/20
Topics: Regular schemes, smooth algebraic varieties
72020.mp4Lecture 17: 7/20/20
Topics: Smooth, flat, and etale morphisms
72220.mp4Lecture 18: 7/22/20
Topics: More on etale morphisms, quasi-coherent sheaves
72720.mp4Lecture 19: 7/27/20
Topics: Pullback of O_X-modules, quasi-coherent sheaves on projective schemes.
72920.mp4Lecture 20: 7/29/20
Topics: Ample sheaves, cohomology
8320.mp4Lecture 21: 8/3/20
Topics: Cech cohomology
8520.pdfLecture 22: 8/5/20
Topics: Cohomology of projective schemes, cohomology of fibers