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arXiv · 2405.13743

Cyclic Cubic Points on Higher Genus Curves

James Rawson
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Abstract

The distribution of degree $d$ points on curves is well understood, especially for low degrees. We refine this study to include information on the Galois group in the simplest interesting case: $d = 3$. For curves of genus at least 5, we show cubic points with Galois group $C_3$ arise from well-structured morphisms, along with providing computable tests for the existence of such morphisms. We prove the same for curves of lower genus under some geometric or arithmetic assumptions.

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James Rawson. 2024-05-22. Cyclic Cubic Points on Higher Genus Curves. https://doi.org/10.1112/jlms.70288

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