Chow-Künneth decomposition for some moduli spaces
In the early 1990's, J. P. Murre proposed a series of conjectures on the complexity of the Chow group of a smooth projective variety, in terms of a motivic Chow-Künneth decomposition on the level of rational equivalence. These conjectures provide a very explicit description of Chow groups in terms of a conjectural descending filtration, called the Bloch-Beilinson filtration. The work under review investigates Murre's Chow-Künneth decomposition conjecture for universal families of smooth curves over spaces which dominate the moduli space \({\mathcal M}_g\), in genus at most \(8\), and show the existence of an equivariant Chow-Künneth decomposition.
scientific article; zbMATH DE number 5554401