Koszul duality and Galois cohomology

Abstract

It it shown that the Bloch-Kato conjecture on the norm residue homomorphism $K^M(F)/l\to H^{\ast }(G_F,Z/l)$ follows from its (partially known) low-degree part under the assumption that the Milnor K-theory algebra $K^M(F)/l$ modulo $l$ is Koszul. This conclusion is a case of a general result on the cohomology of nilpotent (co-)algebras and Koszulity.

arXiv commentAMS-LaTeX v.1.1, 10 pages, no figures. Replaced for tex code correction (%&amslplain added) by request of www-admin

Cited by in corpus (13)

• Koszul algebras and quadratic duals in Galois cohomology
• Galois cohomology of a number field is Koszul
• Koszulity of cohomology = $K(\pi ,1)$-ness + quasi-formality
• The Pure Virtual Braid Group Is Quadratic
• Differential graded Koszul duality: an introductory survey
• Enhanced Koszul properties in Galois cohomology
• Right-angled Artin groups and enhanced Koszul properties
• Mild pro-p groups and the Koszulity conjectures
• One relator maximal pro-p Galois groups and the Koszulity conjectures
• Artin-Tate motivic sheaves with finite coefficients over an algebraic variety
• The algebra of closed forms in a disk is Koszul
• Categorical Bockstein sequences
• Homological full-and-faithfulness of comodule inclusion and contramodule forgetful functors