MATH-482 / 5 credits

Teacher: Lüthi Manuel Werner

Language: English

## Summary

Algebraic number theory is the study of the properties of solutions of polynomial equations with integral coefficients; Starting with concrete problems, we then introduce more general notions like algebraic number fields, algebraic integers, units, ideal class groups...

Rings and fields

## Recommended courses

Galois Theory

Introduction à la théorie analytique des nombres

Rings and modules

## Learning Outcomes

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

• Synthesize the main concepts of algebraic number theory
• Solve problems related to algebraic number theory

## Teaching methods

cours ex-cathedra et exercices

## Expected student activities

De part sa nature, la théorie algébrique des nombres combine des techniques provenant de plusieurs domaines (algebre lineaire, algebre commutative, analyse, geometrie). Il est indispensable d'avoir une bonne maitrise de chacun d'eux. On attend une présence active aux séances de cours et surtout aux séances d'exercices. On demandera notamment aux étudiants de venir presenter leurs solutions au tableau.

## Assessment methods

examen ecrit

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.

## Supervision

 Office hours No Assistants Yes Forum No Others moodle

## Bibliography

Samuel, algebraic number theory

Neukirch, Algebraic Number Theory

## Prerequisite for

Topics in number theory.

Applications of number theory: eg. cryptography

Solving the Birch-Swinnerton-Dyer conjecture and win one of the Millenium Prizes (1M USD) from the  Clay Mathematics Institute.

Receiving the Fields medal

## In the programs

• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Algebraic number theory
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks

## Reference week

 Mo Tu We Th Fr 8-9 MAA330 9-10 10-11 11-12 12-13 13-14 14-15 15-16 MAB111 16-17 17-18 18-19 19-20 20-21 21-22

Wednesday, 8h - 10h: Exercise, TP MAA330

Friday, 15h - 17h: Lecture MAB111