MAGIC038: The algebraic theory of quadratic forms

Course details

Semester

Spring 2008
Monday, January 21st to Friday, March 14th; Monday, April 28th to Friday, May 16th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
0

Timetable

Fridays
12:05 - 12:55

Announcements

A few misprints in the files for the final Lecture 10 (slides and handout) have been corrected and the corrected versions are both on the course webpage now.

Description

Prerequisites

A solid foundation in algebra, including commutative rings, finite fields, and some group theory, as perhaps provided at many UK universities in 3rd year algebra courses on rings and modules or on commutative algebra, and on groups. Some knowledge in noncommutative ring theory might be helpful but isn't essential.

Syllabus

Subject classification: 11E04: Quadratic forms over general fields, 11E81: Algebraic theory of quadratic forms; Witt groups and rings
Syllabus (tentative): - Quadratic forms over general fields and their basic properties: Diagonalization, isometry, isotropy, hyperbolic forms - Witt's theory: Witt cancellation, Witt decomposition - The Witt ring of a field and their structure for certain fields - Quaternion algebras and their norm forms - The Clifford algebra of a quadratic form - The classical invariants of quadratic forms: dimension, discriminant, Clifford invariant - The fundamental ideal and the filtration of the Witt ring - The Cassels-Pfister theorem - round and multiplicative forms, Pfister forms - The Arason-Pfister Hauptsatz - Merkurjev's Theorem - A first glimpse of the Milnor conjecture (Voevodsky's theorem)

Lecturer

  • DH

    Professor Detlev Hoffmann

    University
    University of Nottingham

Bibliography

No bibliography has been specified for this course.

Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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