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 HondaTate 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 DOI:
 10.48550/arXiv.1511.06945
 arXiv:
 arXiv:1511.06945
 Bibcode:
 2015arXiv151106945K
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 11M38;
 14J28
 EPrint:
 11 pages