Lars Halvard Halle

Title:

"Motivic zeta functions of Calabi-Yau varieties"

Abstract:

Let K be a complete discretely valued field with residue field k, and let X be a smooth K-variety 
with trivial canonical sheaf. To such a variety one can associate an invariant known 
as the "motivic zeta function" of X. This is a formal power series with coefficients 
in the Grothendieck ring of k-varieties, which measures how the set of rational points of X 
varies under ramified extension of K.
I will talk about joint work with Johannes Nicaise, where we investigate properties 
of motivic zeta functions. In particular, the case of (semi)abelian varieties will be discussed.