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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.
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- Research Article
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- © The Author(s) 2016
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