One construction of a K3 surface with the dense set of rational points

Mathematics – Algebraic Geometry

Scientific paper

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13 pages; typos corrected, minor changes

Scientific paper

We prove that there exists a number field $K$ and a smooth $\mathrm{K3}$
surface $S_{22}$ over $K$ such that the geometric Picard number of $S_{22}$
equals 1, $S_{22}$ is of genus 12, and the set of $K$-points is Zariski dense
in $S_{22}$.

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