- 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, 2024 to May 30, 2024
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
If there are people who are interested in this class and do not speak Italian, I am happy to deliver this class in English.
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.
Prerequisites: commutative algebra (as treated in the course 06689), projective geometry (as treated in the course 54777), classical algebraic geometry (as treated in the course 96733). Please read the Italian version for a more comprehensive list of prerequisites.
All relevant material appears in the webpage of the course:
https://www.dm.unibo.it/~andrea.petracci3/2024Schemi/
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.petracci3/2024Schemi/
Office hours
See the website of Andrea Petracci