Milnor's conjecture on quadratic forms and mod 2 motivic complexes, by Fabien Morel

Let F be field of characteristic different from 2. In this paper we give a new proof of Milnor's conjecture on the graded ring associated to the powers of the fundamental ideal of the Witt ring of quadratic forms over F, first proven by Orlov, Vishik and Voevodsky. We also use Voevodsky's affirmation of Milnor's conjecture on the mod 2 Galois cohomology of fields. Besides this fact, we only use some elementary homological algebra in the abelian category of Zariski sheaves on the category of smooth k-varieties, involving classical results on sheaves of Witt groups, Rost's cycle modules and sheaves of 0-equidimensional cycles.


Fabien Morel <morel@math.jussieu.fr>