MATH-679 / 3 crédits

Enseignant(s): Patakfalvi Zsolt, Carvajal Rojas Javier Alonso

Langue: Anglais

Remark: This is a course on group schemes with an emphasis on structural theorems for algebraic groups and with a stress on the modern presentation using scheme theory and modern algebrai


Frequency

Every year

Summary

This is a course about group schemes, with an emphasis on structural theorems for algebraic groups (e.g. Barsotti--Chevalley's theorem). All the basics will be covered towards the proof of such theorem, with an estress on the modern presentation using scheme theory and modern algebraic geometry.

Content

Keywords

Group schemes, algebraic groups, Barsotti--Chevalley's theorem, torsors, Picard schemes.

Learning Prerequisites

Required courses

MATH 510 Modern Algebraic Geometry

Learning Outcomes

By the end of the course, the student must be able to:

  • structure of general algebraic groups

Resources

Bibliography

1. Algebraic groups by J. S. Milne.
2. Some structure theorems for algebraic groups by M. Brion.
3. Lectures on the structure of algebraic groups and geometric applications by M. Brion, P. Samueal, and V. Uma.

Ressources en bibliothèque

Dans les plans d'études

  • Forme de l'examen: Mémoire (session libre)
  • Matière examinée: Group schemes
  • Cours: 28 Heure(s)
  • Projet: 14 Heure(s)

Semaine de référence