A census of zeta functions of quartic K3 surfaces over F_2

Abstract

We compute the complete set of candidates for the zeta function of a K3 surface over F_2 consistent with the Weil conjectures, as well as the complete set of zeta functions of smooth quartic surfaces over F_2. These sets differ substantially, but we do identify natural subsets which coincide. This gives some numerical evidence towards a Honda-Tate theorem for transcendental zeta functions of K3 surfaces; such a result would refine a recent theorem of Taelman, in which one must allow an uncontrolled base field extension.

11 pages; final version, minor changes; to appear in ANTS XII

References in corpus (4)

• The Kodaira dimension of the moduli of K3 surfaces
• Good Reduction of K3 Surfaces
• K3 surfaces over finite fields with given L-function
• 2-adic integral canonical models and the Tate conjecture in characteristic 2