Article contents
A census of zeta functions of quartic K
$3$ surfaces over
$\mathbb{F}_{2}$
Published online by Cambridge University Press: 26 August 2016
Abstract
We compute the complete set of candidates for the zeta function of a K$3$ surface over
$\mathbb{F}_{2}$ consistent with the Weil and Tate conjectures, as well as the complete set of zeta functions of smooth quartic surfaces over
$\mathbb{F}_{2}$. 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 K
$3$ surfaces; such a result would refine a recent theorem of Taelman, in which one must allow an uncontrolled base field extension.
MSC classification
- Type
- Research Article
- Information
- Copyright
- © The Author(s) 2016
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20160907143622272-0774:S1461157016000140_inline8.gif?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20160907143622272-0774:S1461157016000140_inline9.gif?pub-status=live)
- 2
- Cited by