Rational points on Atkin–Lehner quotients of geometrically hyperelliptic Shimura curves
نویسندگان
چکیده
Guo and Yang give defining equations for all geometrically hyperelliptic Shimura curves X0(D,N). In this paper we compute the Q-rational points on Atkin–Lehner quotients of these using a variety techniques. We also determine which rational are CM many curves.
منابع مشابه
Rational Points on Atkin-Lehner Quotients of Shimura Curves
We study three families of Atkin-Lehner quotients of quaternionic Shimura curves: X, X 0 (N), and X D+ 1 (N), which serve as moduli spaces of abelian surfaces with potential quaternionic multiplication (PQM) and level N structure. The arithmetic geometry of these curves is similar to, but even richer than, that of the classical modular curves. Two important differences are the existence of a no...
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ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2023
ISSN: ['1878-0792', '0723-0869']
DOI: https://doi.org/10.1016/j.exmath.2023.02.005