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TitleGalois cohomology of a number field is Koszul
Author(s) Leonid Positselski
TypeArticle in Journal
AbstractAbstract 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 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 PBW-bases).
KeywordsGlobal fields, Local fields, Galois cohomology, Koszul algebras, Koszul modules, Class Field Theory, Chebotarev
ISSN0022-314X
URL http://www.sciencedirect.com/science/article/pii/S0022314X1400198X
LanguageEnglish
JournalJournal of Number Theory
Volume145
Pages126 - 152
Year2014
Edition0
Translation No
Refereed No
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