zbMATH — the first resource for mathematics

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].

14C15 (Equivariant) Chow groups and rings; motives
55S20 Secondary and higher cohomology operations in algebraic topology