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A census of zeta functions of quartic K $3$ surfaces over $\mathbb{F}_{2}$
Published Web Location
https://doi.org/10.1112/S1461157016000140No data is associated with this publication.
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.
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