تقرير
Equations of hyperelliptic Shimura curves
| العنوان: | Equations of hyperelliptic Shimura curves |
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| المؤلفون: | Guo, Jia-Wei, Yang, Yifan |
| المصدر: | Compositio Math. 153 (2017) 1-40 |
| سنة النشر: | 2015 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, Mathematics - Algebraic Geometry, Primary 11F03, secondary 11G15, 11G18 |
| الوصف: | By constructing suitable Borcherds forms on Shimura curves and using Schofer's formula for norms of values of Borcherds forms at CM-points, we determine all the equations of hyperelliptic Shimura curves $X_0^D(N)$. As a byproduct, we also address the problem of whether a modular form on Shimura curves $X_0^D(N)/W_{D,N}$ with a divisor supported on CM-divisors can be realized as a Borcherds form, where $X_0^D(N)/W_{D,N}$ denotes the quotient of $X_0^D(N)$ by all the Atkin-Lehner involutions. The construction of Borcherds forms is done by solving certain integer programming problems. Comment: 40 pages, plus 30 pages of tables |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1112/S0010437X16007739 |
| URL الوصول: | http://arxiv.org/abs/1510.06193 |
| رقم الأكسشن: | edsarx.1510.06193 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1112/S0010437X16007739 |
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