On Drinfeld modular curves for SL(2)

Jesse Franklin; Sheng Yang Kevin Ho; Mihran Papikian

doi:10.1142/S0129167X25500442

On Drinfeld modular curves for SL(2)

Jesse Franklin
, Sheng Yang Kevin Ho
, Mihran Papikian

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study the Drinfeld modular curves X₀¹(n) arising from the Hecke congruence subgroups of SL₂(F_q[T]). By using a combinatorial method of Gekeler and Nonnengardt, we obtain a genus formula for these curves. Then, in cases when the genus of X₀¹(n) is one, we compute the Weierstrass equation of the corresponding curve. Finally, we define and study the modular polynomial in this context, which gives a plane singular model of X₀¹(n).

Original language	English (US)
Article number	2550044
Journal	International Journal of Mathematics
Volume	36
Issue number	12
DOIs	https://doi.org/10.1142/S0129167X25500442
State	Published - Oct 1 2025

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1142/S0129167X25500442

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title = "On Drinfeld modular curves for SL(2)",

abstract = "In this paper, we study the Drinfeld modular curves X01(n) arising from the Hecke congruence subgroups of SL2(Fq[T]). By using a combinatorial method of Gekeler and Nonnengardt, we obtain a genus formula for these curves. Then, in cases when the genus of X01(n) is one, we compute the Weierstrass equation of the corresponding curve. Finally, we define and study the modular polynomial in this context, which gives a plane singular model of X01(n).",

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AU - Papikian, Mihran

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N2 - In this paper, we study the Drinfeld modular curves X01(n) arising from the Hecke congruence subgroups of SL2(Fq[T]). By using a combinatorial method of Gekeler and Nonnengardt, we obtain a genus formula for these curves. Then, in cases when the genus of X01(n) is one, we compute the Weierstrass equation of the corresponding curve. Finally, we define and study the modular polynomial in this context, which gives a plane singular model of X01(n).

AB - In this paper, we study the Drinfeld modular curves X01(n) arising from the Hecke congruence subgroups of SL2(Fq[T]). By using a combinatorial method of Gekeler and Nonnengardt, we obtain a genus formula for these curves. Then, in cases when the genus of X01(n) is one, we compute the Weierstrass equation of the corresponding curve. Finally, we define and study the modular polynomial in this context, which gives a plane singular model of X01(n).

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U2 - 10.1142/S0129167X25500442

DO - 10.1142/S0129167X25500442

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JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 12

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ER -

On Drinfeld modular curves for SL(2)

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