Scheme Theory I

Period of duration of course
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Course info
Number of course hours
45
Number of hours of lecturers of reference
40
Number of hours of supplementary teaching
5
CFU 6
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Type of exam

Written and oral exam

Lecturer

View lecturer details

Prerequisites

Commutative algebra, elementary algebraic geometry

Programme

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.

Educational aims

Teaching scheme theory

Bibliographical references

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