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arXiv · 2408.00198

On Drinfeld modular curves for SL(2)

Jesse Franklin·Sheng-Yang Kevin Ho·Mihran Papikian
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Abstract

We study the Drinfeld modular curves arising from the Hecke congruence subgroups of $\mathrm{SL}_2(\mathbb{F}_q[T])$. Using a combinatorial method of Gekeler and Nonnengardt, we obtain a genus formula for these curves. In cases when the genus is one, we compute the Weierstrass equation of the corresponding curve.

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Jesse Franklin, Sheng-Yang Kevin Ho, Mihran Papikian. 2024-07-31. On Drinfeld modular curves for SL(2). https://arxiv.org/abs/2408.00198

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