### On invariants of quadratic forms

#### Zusammenfassung:

In this talk I will first give some
recollection on the Witt ring W(k)of anisotropic quadratic forms over a field k
of char not 2, and will explain the statement of Milnor's conjecture on the
associated graded ring of the filtration of W(k) by the powers of its
fundamental ideal I(k), proven some time ago by Orlov, Vishik and Voevodsky.

I will then explain some simple and new way
to deduce this conjecture from Voevodsky's affirmation of Beilinson-Lichtenbaum
conjecture at the prime 2. Our approach emphasizes elementary use of homological
algebra in the category of (Zariski) sheaves on smooth k-varieties, and also
leads in exactly the same spirit to a rather direct proof of some results of
Arason-Elman producing a presentation of each of the powers I^n(k) of the
fundamental ideal.