English

Equations of Shimura curves of genus 2

Number Theory 2011-11-10 v2 Algebraic Geometry

Abstract

We present explicit models for Shimura curves X_D and Atkin-Lehner quotients X_D/w_m 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.

Keywords

Cite

@article{arxiv.math/0312434,
  title  = {Equations of Shimura curves of genus 2},
  author = {Josep Gonzalez and Victor Rotger},
  journal= {arXiv preprint arXiv:math/0312434},
  year   = {2011}
}

Comments

Some misprints corrected in Table 4.1