A note of functional equations for zeta functions with values in Chow motives (Q2466305)

Varieties with a finite dimensional Chow motive in the sense of Kimura and O'Sullivan have a rational zeta function with coefficinents in the Grothendieck ring of Chow motives. Using the well known decomposition of the Chow motive of an abelian variety, the author deduces a functional equation for the zeta function of an abelian variety. Furthermore investigating the \(\lambda \)-structure of the Grothendieck ring of Chow motives, the author showes that the property of having a rational zeta function satisfying a functional equation is preserved by taking products.