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arXiv · 2311.04353

The automorphisms of certain Kummer surfaces act on the points mod $p$ by the alternating group

Adam Logan·Owen Patashnick
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Abstract

For the family of Kummer surfaces of the square of an elliptic curve over the prime field $\mathbb{F}_p$ with $p$ odd, we show that if the automorphism group acts transitively on the set of points then the action is at least alternating. This is analogous to a result of Meiri, Puder, and Chen arXiv:1702.08358 on the points mod $p$ of the Markoff surface.

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Adam Logan, Owen Patashnick. 2023-11-07. The automorphisms of certain Kummer surfaces act on the points mod $p$ by the alternating group. https://arxiv.org/abs/2311.04353

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