Galois cohomology of a number field is Koszul

JOURNAL OF NUMBER THEORY

卷:145

Article

Positselski, Leonid^1,2,3 

[1] Natl Res Univ Higher Sch Econ, Fac Math, Moscow 117312, Russia

[2] Natl Res Univ Higher Sch Econ, Lab Algebra Geometry, Moscow 117312, Russia

[3] Inst Informat Transmiss Problems, Sect Algebra & Number Theory, Moscow 127994, Russia

关键词: Global fields;    Local fields;    Galois cohomology;    Koszul algebras;    Koszul modules;    Class Field Theory;    Chebotarev's density theorem;    Filtrations on algebras;    Commutative PBW-bases;    Commutative Grobner bases;   

DOI  :  10.1016/j.jnt.2014.05.024

来源: Elsevier

【 摘 要 】

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 Grobner bases (commutative PBW-bases). (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free