Scheme Theory I
Period of duration of course
- Angelo Vistoli
- 050 509310
- Palazzo della Carovana , terzo piano, stanza 68
Commutative algebra, elementary algebraic geometry
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.
Teaching scheme theory
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