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A.Vishik

Algebraic theory of quadratic forms. Connections to Algebraic Geometry and K-theory

Lecture notes

Gzipped postscript (may be viewed directly by some versions of Ghostview)

[Lecture 1 (28K)|Lecture 2 (32K)|Lecture 3 (23K)|Lecture 4 (30K)
Lecture 5 (26K)|Lecture 6 (39K)|Lecture 7 (28K)|Lecture 8 (23K)
Lecture 9 (25K)|Lecture 10 (34K)
Lecture 11 (22K)|Lecture 13 (23K)]

Zipped postscript

[Lecture 1 (28K)|Lecture 2 (32K)|Lecture 3 (23K)|Lecture 4 (30K)
Lecture 5 (26K)|Lecture 6 (39K)|Lecture 7 (28K)|Lecture 8 (23K)
Lecture 9 (26K)|Lecture 10 (34K)
Lecture 11 (22K)|Lecture 13 (23K)]

Syllabus

1. Introduction to the algebraic theory of quadratic forms (here only the notion of elementary algebra is required).
2. Milnor's K-theory of a field, Witt ring of quadratic forms and connection between them (-"-).
3. Quadric as an object of Algebraic geometry, grassmanian of n-planes on a quadric, structure of the Chow motive of a quadric. Consequences for the quadratic form theory. (some familiarity with algebraic geometry is assumed, in particular, with the notion of algebraic cycle and basic operations on them)