Complex multiplication and K3 surfaces over finite fields

Joint IAS/Princeton University Number Theory Seminar
Topic:Complex multiplication and K3 surfaces over finite fields
Speaker:Lenny Taelman
Affiliation:University of Amsterdam
Date:Thursday, April 2
Time/Room:4:30pm - 5:30pm/Fine 214, Princeton University

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 work-in-progress 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.