Algebraic theory of quadratic forms and central simple algebras
Sommersemester 2024
This course is an introduction to the algebraic theory of quadratic forms and central simple algebras over fields. The following topics will be covered: Witt rings, Pfister forms, quadratic forms over extensions of fields, Clifford algebras, Brauer group of a field, Milnor K-theory.
Time and place:
Lectures: Tuesday 12-14 in B252, Friday 12-14 in A027.
Exercises: Thursday 12-14 in B133.
The written exam will take place on Friday 19.07, 12:00-14:00, Room A027.
Exam
Solutions
Literature:
T. Y. Lam, Introduction to Quadratic forms over fields.
R. Elman, N. Karpenko, A. Merkurjev, The algebraic theory of quadratic forms.
B. Kahn, Formes quadratiques sur un corps (available online).
Exercise sheets:
Sheet 1
Sheet 2
Sheet 3
Sheet 4
Sheet 5
Sheet 6
Sheet 7
Sheet 8
Sheet 9
Sheet 10
Sheet 11