Lars Halvard Halle : Motivic zeta functions and the monodromy conjecture for semi-abelian varieties

Posted by Artie Prendergast-Smith , part of the Algebraic Geometry Seminar.

At

May 22, 2013, 4 p.m.

In

SEO 427

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 J. Nicaise, where we investigate motivic zeta functions for semi-abelian varieties. In particular, we prove that the motivic monodromy conjecture holds for these varieties.