Algebraic geometry II - schemes and sheaves
Summary
The aim of this course is to learn the basics of the modern scheme theoretic language of algebraic geometry.
Content
- sheaves
- affine schemes
- general schemes
- projective schemes
- coherent sheaves
- line bundles
- cohomology of sheaves
Learning Prerequisites
Required courses
- Rings and modules
- Algebraic curves
Learning Outcomes
By the end of the course, the student must be able to:
- Use basic notions of scheme theoretic algebraic geometry.
Assessment methods
The final grade will be assigned based on the cumulative points of the student obtained from handed in homework solutions, from homework solutions presented at the exercise sessions and from the written exam. The weights of the two parts are:
30% - handed in homework solutions, and homework presented at the exercise sessions
70% - written exam
Students will have at most 10 homeworks to be handed in, and at most 4 exercises to present at the exercise sessions, throughout the semester.
Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.
Resources
Bibliography
Hartshorne: Algebraic geometry
Ressources en bibliothèque
Moodle Link
Dans les plans d'études
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Algebraic geometry II - schemes and sheaves
- Cours: 4 Heure(s) hebdo x 14 semaines
- Exercices: 4 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Algebraic geometry II - schemes and sheaves
- Cours: 4 Heure(s) hebdo x 14 semaines
- Exercices: 4 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Algebraic geometry II - schemes and sheaves
- Cours: 4 Heure(s) hebdo x 14 semaines
- Exercices: 4 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Algebraic geometry II - schemes and sheaves
- Cours: 4 Heure(s) hebdo x 14 semaines
- Exercices: 4 Heure(s) hebdo x 14 semaines
- Type: optionnel