English

On Drinfeld modular curves for SL(2)

Number Theory 2024-08-02 v1

Abstract

We study the Drinfeld modular curves arising from the Hecke congruence subgroups of SL2(Fq[T])\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.

Keywords

Cite

@article{arxiv.2408.00198,
  title  = {On Drinfeld modular curves for SL(2)},
  author = {Jesse Franklin and Sheng-Yang Kevin Ho and Mihran Papikian},
  journal= {arXiv preprint arXiv:2408.00198},
  year   = {2024}
}

Comments

26 pages

R2 v1 2026-06-28T17:59:55.657Z