### Galois cohomology of a number field is Koszul, by Leonid Positselski

We prove that the Milnor ring of any (one-dimensional) local
or global field K modulo a prime number l is a Koszul algebra
over Z/l. Under mild assumptions that are only needed in the case
l=2, we also prove various module Koszulity properties of this
algebra. This provides evidence in support of Koszulity
conjectures that were proposed in our previous papers. The proofs
are based on the Class Field Theory and computations with
quadratic commutative Groebner bases (commutative PBW-bases).

Leonid Positselski <posic@mccme.ru, positselski@yandex.ru>