On Drinfeld modular curves for SL(2)
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913454867087360 |
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| author | Franklin, Jesse Ho, Sheng-Yang Kevin Papikian, Mihran |
| author_facet | Franklin, Jesse Ho, Sheng-Yang Kevin Papikian, Mihran |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00198 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Drinfeld modular curves for SL(2) Franklin, Jesse Ho, Sheng-Yang Kevin Papikian, Mihran Number Theory 11F06, 11G09, 14G35 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. |
| title | On Drinfeld modular curves for SL(2) |
| topic | Number Theory 11F06, 11G09, 14G35 |
| url | https://arxiv.org/abs/2408.00198 |