MATH-535 / 5 crédits

Enseignant: Chen Eric Yen-Yo

Langue: Anglais

## Summary

This course is aimed to give students an introduction to the theory of algebraic curves, with an emphasis on the interplay between the arithmetic and the geometry of global fields. One of the principle goals will be to understand the geometric formulation of global class field theory.

## Keywords

Algebraic geometry, algebraic curves, global fields, class field theory

## Required courses

• Linear algebra
• Group Theory
• Rings and Modules
• Modern Algebraic geometry

## Recommended courses

• Algebraic topology
• Differential geometry
• Complex Analysis

## Learning Outcomes

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

• Analyze basic problems in algebraic geometry of curves and solve them.
• Use the statements of basic theorems like Riemann-Roch, Serre duality, etc, and understand their proofs
• Reason intuitively about the geometry and topology of curves over the complex and finite fields.

## Teaching methods

2h lectures+2h exercise sessions weekly.

Oral Exam

## Supervision

 Office hours Yes Assistants Yes Forum No

## Bibliography

• Hartshorne, Algebraic Geometry
• R. Miranda, Algebraic Curves and Riemann Surfaces
• J. P. Serre, Algebraic Groups and Class Fields

## Dans les plans d'études

• Semestre: Printemps
• Forme de l'examen: Oral (session d'été)
• Matière examinée: Algebraic geometry III - selected topics
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Oral (session d'été)
• Matière examinée: Algebraic geometry III - selected topics
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Oral (session d'été)
• Matière examinée: Algebraic geometry III - selected topics
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines

## Semaine de référence

 Lu Ma Me Je Ve 8-9 9-10 10-11 MAA330 11-12 12-13 13-14 MAA330 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22

Lundi, 10h - 12h: Cours MAA330

Lundi, 13h - 15h: Exercice, TP MAA330

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