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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

- Introduction to the algebraic theory of quadratic forms
(here only the notion of elementary algebra is required).
- Milnor's K-theory of a field, Witt ring of quadratic forms and
connection between them (-"-).
- 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)