Lectures on Quadratic Forms

Lectures on Quadratic Forms

Date

September 17th, 2019

Location 

Universitat de Barcelona

Lecturer:
Martin Ziegler, Visiting Research Professor, University of Barcelona
 
Course Description: 
This course  is planned as a concise introduction to the classical theory of quadratic forms q over a field F of characteristic different from 2. We start with a detailed discussion of the fundamental theorems of Witt (1937). Then the main methods for the understanding of the Witt ring of a field will be discussed, as Pfister forms, Clifford algebras, the Brauer group, and Milnor’s K-theory. At the end, we will try to give an account of the Milnor conjecture, proved by Voevodsky in 1996.
 
There will be five two-hour sessions during five consecutive weeks. On the 17th of September, in a meeting with the registered people, a suitable schedule for the course will be agreed.
 
Organizer:
Enrique Casanovas (Universitat de Barcelona)

Lectures on Quadratic Forms

Registration form

Date

September 17th, 2019

Location

Universitat de Barcelona

Lecturer:
Martin Ziegler, Visiting Research Professor, University of Barcelona
 
Course Description: 
This course  is planned as a concise introduction to the classical theory of quadratic forms q over a field F of characteristic different from 2. We start with a detailed discussion of the fundamental theorems of Witt (1937). Then the main methods for the understanding of the Witt ring of a field will be discussed, as Pfister forms, Clifford algebras, the Brauer group, and Milnor’s K-theory. At the end, we will try to give an account of the Milnor conjecture, proved by Voevodsky in 1996.
 
There will be five two-hour sessions during five consecutive weeks. On the 17th of September, in a meeting with the registered people, a suitable schedule for the course will be agreed.
 
Organizer:
Enrique Casanovas (Universitat de Barcelona)

Lectures on Quadratic Forms

Registration form

Programme
1. Witt’s theorems
2. The Witt ring of a field
3. Formally real fields
4. Algebraic field extension of F
5. Transcendental field extensions of F
6. Quaternion algebras
7. The Clifford algebra of q
8. The Brauer group of a field
9. Galois cohomology
10. The Milnor conjecture
References
T.Y. Lam. Introduction to quadratic forms over fields, 2005
B. Kahn. Formes quadratiques sur un corps, 2009
Share This