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It it shown that the Bloch-Kato conjecture on the norm residue homomorphism $K^M(F)/l \to H^*(G_F,Z/l)$ 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.Comment: AMS-LaTeX v.1.1, 10 pages, no figures. Replaced for tex code correction (%&amslplain added) by request of www-admi

In this article we describe certain new cohomological operations in algebraic cobordisms. These operations give the natural obstructions for the cobordism class to be represented by the embedding. Also, they permit to work with algebraic cobordisms and Chow groups in a more subtle way than the LandweberNovikov operations (related to 2-torsion effects). We describe applications to the computation of the algebraic cobordisms of a Pfister quadrics and to the problem of rationality of cycles.

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