Schemes

Rutgers MATH 536, Spring 2021.
Algebraic Geometry: schemes and other things


Rational points of bounded height outside the 27 lines on
Clebsch's diagonal cubic surface
Lecture 1 (1/21/2021): Presheaves and sheaves on topological spaces
Lecture 2 (1/28/2021): Locally ringed spaces and the inevitibility of schemes
Lecture 3 (2/4/2021): Schemes
Lecture 4 (2/11/2021): Gluing schemes, Proj
Lecture 5 (2/18/2021): More about Proj, some properties of schemes and morphisms
Lecture 6 (2/25/2021): Fiber products, separated and proper morphisms
Lecture 7 (3/4/2021): Separated and proper morphisms and the valuative criteria
Lecture 8 (3/11/2021): Sheaves of modules, part 1: coherent and quasicoherent sheaves
Lecture 9 (3/25/2021): Sheaves of modules, part 2: more about quasicoherent sheaves
Lecture 10 (4/1/2021): Sheaves of modules, part 3: final comments
Lecture 11 (4/8/2021): Divisors: Weil (and a bit of Cartier)