Details:
Title  Galois cohomology of a number field is Koszul  Author(s)  Leonid Positselski  Type  Article in Journal  Abstract  Abstract We prove that the Milnor ring of any (onedimensional) 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 for arbitrary fields that were proposed in our previous papers. The proofs are based on the Class Field Theory and computations with quadratic commutative Gröbner bases (commutative PBWbases).  Keywords  Global fields, Local fields, Galois cohomology, Koszul algebras, Koszul modules, Class Field Theory, Chebotarev  ISSN  0022314X 
URL 
http://www.sciencedirect.com/science/article/pii/S0022314X1400198X 
Language  English  Journal  Journal of Number Theory  Volume  145  Pages  126  152  Year  2014  Edition  0  Translation 
No  Refereed 
No 
