Galois cohomology of a number field is Koszul

Details Galois cohomology of a number field is Koszul Galois cohomology of a number field is Koszul

2010-07-31

arxiv.org/abs/1008.0095v1

Mathematics

K-Theory and Homology

LaTeX 2e, 23 pages

Scientific paper

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).

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