Fiches de cours

Algebraic K-theory

MATH-488

Enseignant(s) :

Hess Bellwald Kathryn

Langue:

English

Summary

Algebraic K-theory, which to any ring R associates a sequence of groups, can be viewed as a theory of linear algebra over an arbitrary ring. We will study in detail the first two of these groups and applications of algebraic K-theory to number theory, algebraic topology, and representation theory.

Content

  1. K_0 : Grothendieck groups, stability, tensor products, change of rings, the Dévissage, Resolution and Localization theorems and their applications
  2. K_1 : elementary matrices, commutators and determinants, long exact sequences relating K_0 and K_1

Keywords

Rings and modules, Grothendiek group

Learning Prerequisites

Required courses

Second-year algebra and topology courses

Recommended courses

Rings and modules (Anneaux et modules)

Important concepts to start the course

Elementary ring and field theory

Learning Outcomes

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

Transversal skills

Assessment methods

Each student must hand in one exercise each week for correction, which will determine 30% of the final grade.

The student's performance on the final written exam will determine the other 70% of the grade.

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

Websites

Dans les plans d'études

  • Mathématiques - master, 2019-2020, Master semestre 2
    • Semestre
      Printemps
    • Forme de l'examen
      Ecrit
    • Crédits
      5
    • Matière examinée
      Algebraic K-theory
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      2 Heure(s) hebdo x 14 semaines
  • Ingénierie mathématique, 2019-2020, Master semestre 2
    • Semestre
      Printemps
    • Forme de l'examen
      Ecrit
    • Crédits
      5
    • Matière examinée
      Algebraic K-theory
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      2 Heure(s) hebdo x 14 semaines
  • Ingénierie mathématique, 2019-2020, Master semestre 4
    • Semestre
      Printemps
    • Forme de l'examen
      Ecrit
    • Crédits
      5
    • Matière examinée
      Algebraic K-theory
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      2 Heure(s) hebdo x 14 semaines

Semaine de référence

LuMaMeJeVe
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
En construction
Cours
Exercice, TP
Projet, autre

légende

  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand