The kernel of Ribet’s isogeny for genus three Shimura curves

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Title:	The kernel of Ribet’s isogeny for genus three Shimura curves
Author:	Molina Blanco, Santiago; González Rovira, Josep
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres
Abstract:	There are exactly nine reduced discriminants D of indefinite quaternion algebras over Q for which the Shimura curve XD attached to D has genus 3. We present equations for these nine curves. Moreover, for each D we determine a subgroup c(D) of cuspidal divisors of degree zero of the new part of the Jacobian of the modular curve of level D such that the abelian variety quotient by c(D) is the jacobian of the curve XD.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra -Arithmetical algebraic geometry -Shimura varieties -Algebra -Curves, Elliptic -Àlgebra -Corbes modulars -Aritmètica -Varietats de Shimura
Rights:	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Published version Article
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