Scheme Theory I
Prerequisiti
Prerequisites: Commutative algebra, elementary algebraic geometry.
Intended for IV and V year students. Can be taken by PhD students.
Programma
Sheaves on topological spaces. Spectra of rings, Zariski topology. The structure sheaf. Schemes. Morphisms between schemes.
Topological properties of schemes. Noetherian schemes. Dimension.
Quasi-coherent sheaves, and operations on them. Invertible sheaves. Divisors. Maps into projective spaces.
Finite morphisms. Normalization.
Obiettivi formativi
Teaching the basics of scheme theory.
Riferimenti bibliografici
Qing Liu, Algebraic Geometry and Arithmetic Curves, Oxford University Press
Robin Hartshorne, Algebraic Geometry, Springer–Verlag
David Mumford, The Red Book of Varieties and Schemes, Lecture Notes in Mathematics, Springer–Verlag
David Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer–Verlag
David Eisenbud, Joe Harris, Geometry of Schemes, Springer–Verlag