Complex Multiplication and K3 Surfaces over Finite Fields
Complex Multiplication and K3 Surfaces over Finite Fields

Lenny Taelman, University of Amsterdam
Fine Hall 214
In this talk I will review CM theory of complex projective K3 surfaces, and show how it can be used to construct K3 surfaces over finite fields. I will discuss workinprogress where this is applied to describing: (1) the collection of zeta functions of K3 surfaces over a finite field, and (2) the category of ordinary K3 surfaces over a finite field. These are similar to theorems of Honda and Tate resp. Deligne on abelian varieties over finite fields.