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arXiv:math/0312434 [math.NT]AbstractReferencesReviewsResources

Equations of Shimura curves of genus 2

Josep Gonzalez, Victor Rotger

Published 2003-12-23, updated 2007-07-20Version 2

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.

Comments: Some misprints corrected in Table 4.1
Journal: International Mathematics Reserach Notices, 14 (2004)
Categories: math.NT, math.AG
Subjects: 11G18, 14G35
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