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Symmetric operations. (English. Russian original) Zbl 1117.14007
Proc. Steklov Inst. Math. 246, 79-92 (2004); translation from Tr. Mat. Inst. Steklova 246, 92-105 (2004).
Let $$X$$ be a smooth projective variety over a field $$\kappa$$ of characteristic zero and let $$\text{pr}:\Omega^*(X)\to \text{CH}^*(X)$$ be the natural ring epimorphism from the algebraic cobordism ring $$\Omega^*(X)$$ to the Chow ring $$\text{CH}^*(X)$$ [M. Levine and F. Morel, C. R. Acad. Sci., Paris, Sér. I, Math. 332, No. 8, 723–728 (2001; Zbl 0991.19001)]. The article under review constructs certain natural cohomological operations on $$\Omega^*(X)$$ which, after composition with the morphism pr, coincide in $$\text{CH}^*(X)$$ with the halves of the Chow traces of certain Landweber-Novikov operations. Furthermore, those operations in $$\Omega^*(X)$$ produce new operations between the Chow rings of two varieties that cannot be reduced to Steenrod operations.
For the entire collection see [Zbl 1087.14002].

##### MSC:
 14C15 (Equivariant) Chow groups and rings; motives 55S20 Secondary and higher cohomology operations in algebraic topology
##### Keywords:
cohomological operations; algebraic cobordism; Chow ring