[This preprint has been superceded by 0720.]
We propose a conjecture on the homological properties of the Milnor K-theory algebra with Z/l coefficients of an arbitrary field F which implies both the Bloch-Kato conjecture (claiming that the norm residue map to the Galois cohomology is an isomorphism) and Bogomolov's conjecture (that the commutator subgroup of the maximal quotient pro-l-group of the Galois group is free).
A parallel case of the Milnor K-theory with Q coefficients of a field F of finite characteristic, where a conjecture of Goncharov plays the role of Bogomolov's conjecture, is briefly considered in the Introduction.
This paper is a continuation of my paper with Alexander Vishik published in Math. Research Letters in 1995 (alg-geom/9507010), where we proved that if the Milnor algebra modulo l has the Koszul property then the Bloch-Kato conjecture follows from its low-degree part.