Luigi Pagano

Motivic zeta functions and the monodromy conjecture

In this talk we deal witht the motivic zeta function attached to Calabi-Yau varieties defined over a field K endowed with an ultrametric absolute value. I will explain what does it mean for a formal series with coefficients in the Grothendieck ring of varieties to be rational and how poles are defined. I will finally discuss the monodromy conjecture that relates those poles with the action of the absolute Galois group of K on the (étale) cohomology of X.