Complex Multiplication and K3 Surfaces over Finite Fields

Complex Multiplication and K3 Surfaces over Finite Fields

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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 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.