- Docente: Andrea Petracci
- Credits: 6
- SSD: MAT/03
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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from Feb 20, 2023 to May 25, 2023
Learning outcomes
At the end of this course, the student knows the basic notions of scheme theory. These can be applied in their research field in algebra and geometry.
Course contents
Scheme theory, which was developed by Alexander Grothendieck, is the modern and rigorous language with which one studies algebraic geometry. It unifies classical algebraic geometry and algebraic number theory.
The topics of this class include: sheaves, schemes, global and local properties of schemes, coherent sheaves, sheaf cohomology.
Necessary prerequisite: commutative algebra (as treated in the course 06689).
It is recommended that the student has some familiarity with basic notions of algebraic geometry, in particular:
- projective space and plane algebraic curves (as treated in the course 54777)
- geometry of affine varieties and of quasi-projective varieties (as treated in the first chapter of the book by Hartshorne, or in the first part of the courses 96733 and 66734).
More precise information can be found in the webpage of the last year: https://www.dm.unibo.it/~andrea.petracci3/2023Schemi/
Readings/Bibliography
Hartshorne, Algebraic geometry, GTM 52, Springer
Liu, Algebraic Geometry and Arithmetic Curves, Oxford Graduate Texts in Mathematics
Other sources:
Mumford, The Red Book of Varieties and Schemes, Springer
Eisenbud & Harris, The geometry of schemes, GTM 197, Springer
Görtz & Wedhorn, Algebraic geometry, I & II, Vieweg+Teubner
Teaching methods
Blackboard lectures
Assessment methods
Homework + Oral exam
Links to further information
https://www.dm.unibo.it/~andrea.petracci3/2023Schemi/
Office hours
See the website of Andrea Petracci