Adams operations and power structures

Details Adams operations and power structures Adams operations and power structures

2008-03-21

arxiv.org/abs/0803.3118v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

We construct a family of additive endomorphisms $\Psi_k, k=1, 2...$ of the Grothendieck ring of quasiprojective varieties and the Grothendieck ring of Chow motives similar to the Adams operations in the K-theory. The speciality of the $\lambda$-structure on the Grothendieck ring of motives (proved by F. Heinloth) gives a set of natural equations for these operations. We discuss this construction in a general setting and relate it to the concept of power structures introduced by S. Gusein-Zade, I. Luengo and A. Melle-Hernandez. Some interpretation of the E. Getzler's formula for the equivariant Hodge-Deligne polynomial of the configuration spaces is also discussed.

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