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arXiv · 1511.06945

A census of zeta functions of quartic K3 surfaces over F_2

Kiran S. Kedlaya·Andrew V. Sutherland
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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.

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Kiran S. Kedlaya, Andrew V. Sutherland. 2016-05-16. A census of zeta functions of quartic K3 surfaces over F_2. https://doi.org/10.1112/s1461157016000140

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