Equations of Shimura Curves of Genus
نویسنده
چکیده
We present explicit models for Shimura curves X D and Atkin-Lehner quotients X D /ωm of them of genus 2. We show that several equations conjectured by Kurihara are correct and compute for them the kernel of Ribet's isogeny J 0 (D) new → J D between the new part of the Jacobian of the modular curve X 0 (D) and the Jacobian of X D .
منابع مشابه
Equations of Shimura Curves of Genus Two
LetBD be the indefinite quaternion algebra overQ of reduced discriminantD=p1· · · · ·p2r for pairwise different prime numbers pi and let XD/Q be the Shimura curve attached to BD. As it was shown by Shimura [23], XD is the coarse moduli space of abelian surfaces with quaternionic multiplication by BD. Let W = {ωm : m | D} ⊆ Aut Q(XD) be the group of Atkin-Lehner involutions. For any m | D, we wi...
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