Coursebooks

Algebraic K-theory

MATH-488

Lecturer(s) :

Hess Bellwald Kathryn

Language:

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

In the programs

  • Mathematics - master program, 2019-2020, Master semester 2
    • Semester
      Spring
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Algebraic K-theory
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Applied Mathematics, 2019-2020, Master semester 2
    • Semester
      Spring
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Algebraic K-theory
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Applied Mathematics, 2019-2020, Master semester 4
    • Semester
      Spring
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Algebraic K-theory
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks

Reference week

MoTuWeThFr
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
Under construction
Lecture
Exercise, TP
Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German