Holmstrom Motivic Chow series

arXiv:0909.5232 Rationality of motivic Chow series modulo A^1-homotopy from arXiv Front: math.AG by E. Javier Elizondo, Shun-ichi Kimura Consider the formal power series $\sum [C_{p, \alpha}(X)]t^{\alpha}$ (called Motivic Chow Series), where $C_p(X)=\disjoint C_{p, \alpha}(X)$ is the Chow variety of $X$ parametrizing the $p$-dimensional effective cycles on $X$ with $C_{p, \alpha}(X)$ its connected components, and $[C_{p, \alpha}(X)]$ its class in $K(ChM)_{A^1}$, the $K$-ring of Chow motives modulo $A^1$ homotopy. Using Picard product formula and Torus action, we will show that the Motivic Chow Series is rational in many cases.

nLab page on Motivic Chow series